%% book.bib - contains BiBtex input for the bibliography of the book @article{smets93dis, author = "Ph. Smets", title = "Belief functions: the disjunctive rule of combination and the generalized {B}ayesian theorem", journal= "International Journal of Approximate reasoning", volume = "9", pages = "1--35", year = "1993" } @book{vonneumann44, author = "J. von Neumann and O. Morgenstern", title = "Theory of Games and Economic Behavior", publisher= "Princeton University Press", year = "1944" } @book{Mates72, author = "B. Mates", title = "Elementary Logic", publisher = "Oxford University Press", year = "1972"} @INPROCEEDINGS{Saffiotti_abelief-function, author = {Alessandro Saffiotti}, title = {A Belief-Function Logic}, booktitle = {Universit Libre de Bruxelles}, year = {}, pages = {642--647}, publisher = {MIT Press} } @inproceedings{cuzzolin09ecsqaru, author = {F. Cuzzolin}, title = {Complexes of outer consonant approximations}, booktitle = {Proceedings of ECSQARU'09}, year = {2009}} @article{cuzzolin09smcb, author = "F. Cuzzolin", title = "Credal semantics of Bayesian transformations in terms of probability intervals", journal= "IEEE Transactions on Systems, Man, and Cybernetics - Part B (to appear)", year = "2009" } @inproceedings{haenni05isipta, author = {R. Haenni}, title = {Towards a Unifying Theory of Logical and Probabilistic Reasoning}, booktitle = {Proceedings of ISIPTA'05}, year = {2005}} @inproceedings{seidenfeld07isipta, Author = {T. Seidenfeld and M. Schervish and J. Kadane}, Booktitle = {Proceedings of ISIPTA'07}, Title = {Coherent Choice Functions under Uncertainty}, Year = {2007}} @book{levi80book, author = "I. Levi", title = "The enterprise of knowledge: An essay on knowledge, credal probability, and chance", publisher= "The MIT Press", address= "Cambridge, Mass.", year = "1980" } @inproceedings{HRWW08a, Address = {Ishikawa, Japan}, Author = {R. Haenni and J.W. Romeijn and G. Wheeler and J. Williamson}, Booktitle = {{UncLog'08}, International Workshop on Interval/Probabilistic Uncertainty and Non-Classical Logics}, Editor = {V. N. Huynh and Y. Nakamori and H. Ono and J. Lawry and V. Kreinovich and H. T. Nguyen}, Number = {46}, Pages = {268--279}, Series = {Advances in Soft Computing}, Title = {Possible Semantics for a Common Framework of Probabilistic Logics}, Bdsk-File-1 = {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}, Bdsk-File-2 = {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}}, Year = {2008}} @article{denoeux07ai, author = "T. Denoeux", title = "Conjunctive and disjunctive combination of belief functions induced by non distinct bodies of evidence", journal= "Artificial Intelligence", year = "2007" } @article{dubois86set, author = "D. Dubois and H. Prade", title = "A set-theoretic view of belief functions: logical operations and approximations by fuzzy sets", journal= "Int. J. of General Systems", volume = "12", pages = "193–-226", year = "1986" } @inproceedings{denoeux08flairs, author = {T. Denoeux}, title = {A new justification of the unnormalized {D}empster’s rule of combination from the {L}east {C}ommitment {P}rinciple}, booktitle = {Proceedings of FLAIRS'08, Special Track on Uncertaint Reasoning}, year = {2008} } @article{lehrer05updating, author = "E. Lehrer", title = "Updating non-additive probabilities — a geometric approach", journal= "Games and Economic Behavior", volume = "50", pages = "42--57", year = "2005" } @INPROCEEDINGS{dezert, AUTHOR = "J. Dezert and F. Smarandache", TITLE = "A new probabilistic transformation of belief mass assignment", YEAR = "2007" } @book{unclog08book, editor = "V.-N. Huynh and Y. Nakamori and H. Ono and J. Lawry and V. Kreinovich and H.T. Nguyen", title = "Interval / Probabilistic Uncertainty and Non-Classical Logics ", publisher= "Springer", year = "2008" } @INPROCEEDINGS{sudano03icif, AUTHOR = "J.J. Sudano", TITLE = "Equivalence Between Belief Theories and Naïve Bayesian Fusion for Systems with Independent Evidential Data", BOOKTITLE = "Proceedings of the Sixth International Conference on Information Fusion (ISIF'03)", YEAR = "2003" } @article{zaffalon04incomplete, author = {Gert de Cooman and Marco Zaffalon}, title = {Updating beliefs with incomplete observations}, journal = {Artif. Intell.}, volume = {159}, number = {1-2}, year = {2004}, issn = {0004-3702}, pages = {75--125}, doi = {http://dx.doi.org/10.1016/j.artint.2004.05.006}, publisher = {Elsevier Science Publishers Ltd.}, address = {Essex, UK}, } @article{yager86entailment, author = "R.R. Yager", title = "The entailment principle for {D}empster-{S}hafer granules", journal= "International Journal of Intelligent Systems", volume = "1", pages = "247--262", year = "1986" } @article{dubois86logical, author = "D. Dubois and H. Prade", title = "A set-theoretic view of belief functions: Logical operations and approximations by fuzzy sets", journal= "International Journal of General Systems", volume = "12", pages = "193–-226", year = "1986" } @article{bruning02stat, author = "M. Bruning and D. Denneberg", title = "Max-min $\sigma$-additive representation of monotone measures", journal= "Statistical Papers", volume = "34", pages = "23--35", year = "2002" } @article{Cobb03isf, author = "B.R. Cobb and P.P. Shenoy", title = "A comparison of {B}ayesian and belief function reasoning", journal= "Information Systems Frontiers", volume = "5", number = "4", pages = "345--358", year = "2003" } @TechReport{haduong06climate, author={M. Ha-Duong}, title={Hierarchical fusion of expert opinion in the Transferable Belief Model, application on climate sensivity}, year = {2006}, institution={HAL}, type={Working Papers}, number={halshs-00112129-v3} } @inproceedings{guironnet06eusipco, author = {M. Guironnet and D. Pellerin and Mich`ele Rombaut}, title = {Camera motion classification based on the transferable belief model}, booktitle = {Proceedings of EUSIPCO'06, Florence, Italy}, year = {2006}} @article{cuzzolin07ai, author = "F. Cuzzolin", title = "Rationale and Properties of the Intersection Probability", journal= "submitted to Artificial Intelligence Journal", year = "2009" } @inproceedings{cuzzolin08jelia, author = {F. Cuzzolin}, title = {On the structure of simplex of inner {B}ayesian approximations}, booktitle = {Proceedings of the European Conference on Logics in Artificial Intelligence (JELIA'08), Dresden, Germany}, year = {2008}} @article{weiler94approximation, author = "T. Weiler", title = "Approximation of belief functions", journal= "IJUFKS", volume = "11", number = "6", pages = "749--777", year = "2003" } @incollection{paris08unclog, author = "Jeff B. Paris and David Picado-Muino and Michael Rosefield", title = "Information from inconsistent knowledge: A probability logic approach", booktitle = "Interval / Probabilistic Uncertainty and Non-classical Logics, Advances in Soft Computing", volume = "46", publisher = "Springer-Verlag, Berlin - Heidelberg", editor = "V.-N. Huynh and Y. Nakamori and H. Ono and J. Lawry and V. Kreinovich and H.T. Nguyen", year = "2008"} @incollection{batens00, author = "D. Batens and C. Mortensen and G. Priest", title = "Frontiers of paraconsistent logic", booktitle = "Studies in logic and computation", volume = "8", publisher = "Research Studies Press", editor = "J.P. Van Bendegem", year = "2000"} @book{priest89, author = "G. Priest and R. Routley and J. Norman", title = "Paraconsistent logic: Essays on the inconsistent", publisher = "Philosophia Verlag ", year = "1989"} @inproceedings{cliff92minimal, author = "C. Joslyn and G. Klir", title = "Minimal Information Loss Possibilistic Approximations of Random Sets", booktitle = "Proc. 1992 FUZZ-IEEE Conference, San Diego", pages = "1081--1088", year = "1992" } @article{Cobb03isf, author = "B.R. Cobb and P.P. Shenoy", title = "A comparison of {B}ayesian and belief function reasoning", journal= "Information Systems Frontiers", volume = "5", number = "4", pages = "345--358", year = "2003" } @article{cuzzolin04smc, author = "F. Cuzzolin", title = "Geometry of {D}empster's rule of combination", journal= "IEEE Transactions on Systems, Man and Cybernetics part B", volume = "34", number = "2", pages = "961--977", year = "2004" } @article{cuzzolin10smcb, author = "F. Cuzzolin", title = "On consistent belief functions", journal= "submitted to the IEEE Transactions on Systems, Man and Cybernetics - part B", year = "2010" } @inproceedings{cuzzolin08unclog-semantics, author = {F. Cuzzolin}, title = {Semantics of the relative belief of singletons}, booktitle = {International Workshop on Uncertainty and Logic UNCLOG'08, Kanazawa, Japan}, year = {2008}} @INPROCEEDINGS{sudano01icif, AUTHOR = "J.J. Sudano", TITLE = "Pignistic Probability Transforms for Mixes of Low- and High-Probability Events", BOOKTITLE = "Proceedings of the Fourth International Conference on Information Fusion (ISIF'01), Montreal, Canada", pages = "23--27", YEAR = "2001" } @INPROCEEDINGS{cuzzolin08pricai, AUTHOR = "F. Cuzzolin", TITLE = "Dual properties of the relative belief of singletons", BOOKTITLE = "Proceedings of the Tenth Pacific Rim Conference on Artificial Intelligence (PRICAI'08), Hanoi, Vietnam, December 15-19 2008", YEAR = "2008" } @article{cuzzolin08smcc, author = "F. Cuzzolin", title = "A geometric approach to the theory of evidence", journal= "IEEE Transactions on Systems, Man, and Cybernetics - Part C", volume = "38", number = "4", pages = "522--534", year = "2008" } @article{decampos94, author = "L. de Campos and J. Huete and S. Moral", title = "Probability intervals: a tool for uncertain reasoning", journal= "Int. J. Uncertainty Fuzziness Knowledge-Based Syst.", volume = "1", pages = "167--196", year = "1994" } @book{levi80enterprise, author = "I. Levi", title = "The enterprise of knowledge", publisher= "MIT Press", year = "1980" } @article{tessem92interval, author = "B. 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Cattaneo}, title = {Combining Belief Functions Issued from Dependent Sources.}, booktitle = {ISIPTA}, year = {2003}, pages = {133-147}, ee = {http://www.carleton-scientific.com/isipta/PDF/011.pdf}, bibsource = {DBLP, http://dblp.uni-trier.de}} @inproceedings{wierman01measuring, author = {M.J. Wierman}, title = {Measuring conflict in evidence theory}, booktitle = {Proceedings of the Joint 9th IFSA World Congress, Vancouver, BC, Canada}, volume = {3}, year = {2001}, pages = {1741-1745}} @article{lefevre02if, author = "E. Lefevre and O. Colot and P. Vannoorenberghe", title = "Belief functions combination and conflict management", journal= "Information Fusion Journal", volume = "3", number = "2", pages = "149--162", year = "2002" } @inproceedings{josang03strategies, author = {A. Josang and M. Daniel and P. Vannoorenberghe}, title = {Strategies for Combining Conflicting Dogmatic Beliefs}, booktitle = {Proceedings of Fusion 2003}, volume = {2}, year = {2003}, pages = {1133-1140}} @incollection{dubois92various, author = "D. Dubois and H. Prade", title = "On the combination of evidence in various mathematical frameworks", booktitle = "Reliability Data Collection and Analysis", editor = "J. flamm and T. Luisi", pages = "213-241", publisher= "", year = "1992" } @article{smets90pami, author = "Ph. Smets", title = "The combination of evidence in the transferable belief model", journal= "IEEE Tr. PAMI", volume = "12", pages = "447--458", year = "1990" } @article{yager87new, author = "R.R. Yager", title = "On the {D}empster-{S}hafer framework and new combination rules", journal= "Information Sciences", volume = "41", pages = "93--138", year = "1987" } @article{zadeh86simple, author = "L. 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Lingras", title = "Interpretations of belief functions in the theory of rough sets", journal= "Information Sciences", volume = "104(1-2)", pages = "81--106", year = "1998" } @article{yao98comparative, author = "Y. Y. Yao", title = "A comparative study of fuzzy sets and rough sets", journal= "Information Sciences", volume = "109(1-4)", pages = "227--242", year = "1998" } @article{1163941, author = {W. Liu}, title = {Analyzing the degree of conflict among belief functions}, journal = {Artif. Intell.}, volume = {170}, number = {11}, year = {2006}, issn = {0004-3702}, pages = {909--924}, doi = {http://dx.doi.org/10.1016/j.artint.2006.05.002}, publisher = {Elsevier Science Publishers Ltd.}, address = {Essex, UK}, } @article{hunter06fusion, author = " A. Hunter and W. Liu", title = "Fusion rules for merging uncertain information", journal= "Information Fusion", volume = "7(1)", pages = "97--134", year = "2006" } @article{yager87on, author = "R. R. Yager", title = "On the Dempster-Shafer framework and new combination rules", journal= "Information Sciences", volume = "41", pages = "93--138", year = "1987" } @article{smets81degree, author = "Ph. Smets", title = "The Degree of Belief in a Fuzzy Event", journal= "Information Sciences", volume = "25", pages = "1--19", year = "1981" } @article{smets91varieties, author = "Ph. Smets", title = "Varieties of ignorance", journal= "Information Sciences", volume = "57-58", pages = "135--144", year = "1991" } @article{grabish06lattices, author = "M. Grabisch", title = "Belief functions on lattices", journal= "Int. J. of Intelligent Systems", volume = "", pages = "", year = "2006" } @article{grabish06moebius, author = "M. Grabisch", title = "The {M}oebius transform on symmetric ordered structures and its application to capacities on finite sets", journal= "Discrete Mathematics", volume = "287 (1-3)", pages = "17--34", year = "2004" } @article{honda06entropy, author = "A. Honda and M. Grabisch", title = "Entropy of capacities on lattices and set systems", journal= "To appear in Information Science", volume = "", pages = "", year = "2006" } @article{DBLP:journals/isci/RamerK93, author = {A. Ramer and G. J. Klir}, title = {Measures of discord in the {D}empster-{S}hafer theory.}, journal = {Information Sciences}, volume = {67}, number = {1-2}, year = {1993}, pages = {35-50}, ee = {http://dx.doi.org/10.1016/0020-0255(93)90083-X}, bibsource = {DBLP, http://dblp.uni-trier.de} } % ------------- @inproceedings{dubois01isipta, author = {Didier Dubois and Henri Prade and Philippe Smets}, title = {New semantics for quantitative possibility theory.}, booktitle = {ISIPTA}, year = {2001}, pages = {152-161}, ee = {http://ippserv.ugent.be/$\sim$isipta01/proceedings/019.html}, crossref = {DBLP:conf/isipta/2001}, bibsource = {DBLP, http://dblp.uni-trier.de} @misc{dubois93possibilityprobability, author = "D. Dubois and H. Prade and S. Sandri", title = "On possibility/probability transformations", text = "D. Dubois, H. Prade and S. Sandri, On possibility/probability transformations, in Fuzzy Logic: State of the Art (R. Lowen, M. Roubens, eds.), Kluwer Academic Publ., Dordrecht, 1993, 103-112.", year = "1993", url = "citeseer.ist.psu.edu/dubois93possibilityprobability.html" } @inproceedings{cliff92minimal, author = "C. Joslyn and G. Klir", title = "Minimal Information Loss Possibilistic Approximations of Random Sets", booktitle = "Proc. 1992 FUZZ-IEEE Conference", editor = "Jim Bezdek", pages = "1081--1088", location = "San Diego", year = "1992", url = "citeseer.ist.psu.edu/joslyn92minimal.html" } @inproceedings{joslyn91towards, author = "C. Joslyn", title = "Towards an empirical semantics of possibility through maximum uncertainty", booktitle = "Proc. IFSA 1991", volume = "A", editor = "R. Lowen and M. Roubens", pages = "86--89", location = "Brussels", year = "1991" } @article{joslyn97possibilistic, author = "C. Joslyn", title = "Possibilistic normalization of inconsistent random intervals", journal= "Advances in Systems Science and Applications", volume = "", pages = "44--51", year = "1997" } @book{almond95book, author = "R. G. Almond", title = "Graphical Belief Modeling", publisher= "Chapman and Hall/CRC", address= "", year = "1995" } @article{lo06mss, author = "K. C. Lo", title = "Agreement and stochastic independence of belief functions", journal= "Mathematical Social Sciences", volume = "51(1)", pages = "1-22", year = "2006" } @article{demotier06smcc, author = "S. Demotier and W. Schon and T. Denoeux", title = "Risk assessment based on weak information using belief functions: a case study in water treatment", journal= "IEEE Transactions on Systems, Man and Cybernetics, Part C", volume = "36(3)", pages = "382- 396", year = "May 2006" } @inproceedings{quost06ipmu, author = {B. Quost and T. Denoeux, and M. Masson}, title = {One-against-all Classifier Combination in the Framework of Belief Functions}, booktitle = {IPMU}, year = {2006}, pages = {} } @inproceedings{quost06ipmu, author = {A. Ben Yaghlane and T. Denoeux and K. Mellouli}, title = {Elicitation of Expert Opinions for Constructing Belief Functions}, booktitle = {IPMU}, year = {2006}, pages = {} } @inproceedings{denoeux06ipmu, author = {T. Denoeux}, title = {Construction of predictive belief functions using a frequentist approach}, booktitle = {IPMU}, year = {2006}, pages = {} } @inproceedings{josang06ipmu, author = {Audun Josang and Simon Pope and David McAnally}, title = {Normalising the Consensus Operator for Belief Fusion}, booktitle = {IPMU}, year = {2006}, pages = {} } @inproceedings{schubert06ipmu, author = {Johan Schubert}, title = {Managing decomposed belief functions}, booktitle = {IPMU}, year = {2006}, pages = {} } @inproceedings{come06ipmu, author = {Etienne Côme and Laurent Bouillaut and Patrice Aknin and Same Allou}, title = {Bayesian Network for railway infrastructure diagnosis}, booktitle = {IPMU}, year = {2006}, pages = {} } @inproceedings{mercier06ipmu, author = {D. Mercier and T. Denoeux and M. Masson}, title = {Refined sensor tuning in the belief function framework using contextual discounting}, booktitle = {IPMU}, year = {2006}, pages = {} } @inproceedings{yaghlane06ipmu, author = {B. Ben Yaghlane and K. Mellouli}, title = {Belief Function Propagation in Directed Evidential Networks}, booktitle = {IPMU}, year = {2006}, pages = {} } @article{ristic06if, author = "B. Ristic and Ph. Smets", title = "The {TBM} global distance measure for the association of uncertain combat {ID} declarations", journal= "Information Fusion", volume = "7(3)", pages = "276-284", year = "2006" } @inproceedings{miranda04ipmu, author = {P. Miranda and M. Grabisch and P. Gil}, title = {On some Results of the Set of Dominating k-additive Belief Functions}, booktitle = {IPMU}, year = {2004}, pages = {625-632} } @inproceedings{ristic04ipmu, author = {B. Ristic and P. Smets}, title = {Belief Function Theory on the Continuous Space with an Application to Model Based Classification}, booktitle = {IPMU}, year = {2004}, pages = {1119-1126} } @inproceedings{baroni04ipmu, author = {P. Baroni}, title = {Extending Consonant Approximations to Capacities}, booktitle = {Proceedings of IPMU}, year = {2004}, pages = {1127-1134} } @inproceedings{daniel04ipmu, author = {M. Daniel}, title = {Consistency of Probabilistic Transformations of Belief Functions}, booktitle = {Proceedings of IPMU}, year = {2004}, pages = {1135-1142} } @inproceedings{/isipta/Cattaneo03, author = {Marco E. G. V. Cattaneo}, title = {Combining Belief Functions Issued from Dependent Sources.}, booktitle = {ISIPTA}, year = {2003}, pages = {133-147}, ee = {http://www.carleton-scientific.com/isipta/PDF/011.pdf}, crossref = {DBLP:conf/isipta/2003}, bibsource = {DBLP, http://dblp.uni-trier.de} @article{shafer82parametric, author = "G. Shafer", title = "Belief functions and parametric models", journal= "Journal of the Royal Statistical Society, Series B", volume = "44", pages = "322-352", year = "1982" } @article{daniel06on, author = "M. Daniel", title = "On Transformations of Belief Functions to Probabilities", journal= "International Journal of Intelligent Systems, special issue on Uncertainty Processing", editor = "Radim Jirouek and Gernot D. Kleiter and Jiina Vejnarová" volume = "21(3)", pages = "261 - 282", year = "February 2006" } @incollection{ha98geometric, author = "V. Ha and P. Haddawy", title = "Geometric Foundations for Interval-Based Probabilities", booktitle = "{KR}'98: Principles of Knowledge Representation and Reasoning", address = "San Francisco, California", editor = "Anthony G. Cohn and Lenhart Schubert and Stuart C. Shapiro", pages = "582--593", year = "1998", url = "citeseer.ist.psu.edu/ha98geometric.html" } @article{cuzzolin06consonant, author = "F. Cuzzolin", title = "The geometry of consonant belief functions: simplicial complexes of necessity measures", journal= "Fuzzy Sets and Systems", year = "2010" } @article{cuzzolin05amai, author = "F. Cuzzolin", title = "Algebraic structure of the families of compatible frames of discernment", journal= "Annals of Mathematics and Artificial Intelligence", volume = "45(1-2)", pages = "241-274", year = "2005" } @article{Chateauneuf89, author = "A. Chateauneuf and J.Y. Jaffray", title = "Some characterization of lower probabilities and other monotone capacities through the use of Möbius inversion", journal= "Math. Soc. Sci.", volume = "17", pages = "263-283", year = "1989" } @INPROCEEDINGS{ubf, AUTHOR = "Philippe Smets ", TITLE = "The Nature of the Unnormalized Beliefs Encountered in the Transferable Belief Model", BOOKTITLE = "Proceedings of the 8th Annual Conference on Uncertainty in Artificial Intelligence (UAI-92)", PUBLISHER = "Morgan Kaufmann", ADDRESS = "San Mateo, CA", YEAR = "1992", PAGES = "292-29" } @misc{ zaffalon-treebased, author = "Marco Zaffalon and Enrico Fagiuoli", title = "Tree-Based Credal Networks for Classification", url = "citeseer.ist.psu.edu/579709.html" } @book{halpern03book, author = "J.Y. Halpern", title = "Reasoning About Uncertainty", publisher= "MIT Press", address= "", year = "2003" } @book{walley91book, author = "P. Walley", title = "Statistical Reasoning with Imprecise Probabilities", publisher= "Chapman and Hall", address= "New York", year = "1991" } @book{shafer01book, author = "Glenn Shafer and Vladimir Vovk", title = "Probability and Finance: It's Only a Game!", publisher= "Wiley", address= "New York", year = "2001" } @inproceedings{cuzzolin05hawaii, author = "F. Cuzzolin", title = "On the properties of relative plausibilities", booktitle= "Proceedings of the International Conference of the IEEE Systems, Man, and Cybernetics Society (SMC'05), Hawaii, USA" editor = "", journal= "", volume = "", pages = "", year = "October 10-12, 2005" } @inproceedings{cuzzolin04ipmu, author = "F. Cuzzolin", title = "Simplicial complexes of finite fuzzy sets", booktitle= "Proceedings of the $10^{th}$ International Conference on Information Processing and Management of Uncertainty IPMU'04, Perugia, Italy", editor = "", journal= "", volume = "", pages = "1733-1740", year = "2004" } @inproceedings{cuzzolin06ipmu, author = "F. Cuzzolin", title = "The geometry of relative plausibilities", booktitle = "Proceedings of the $11^{th}$ International Conference on Information Processing and Management of Uncertainty IPMU'06, special session on ``Fuzzy measures and integrals, capacities and games", Paris, France", editor = "", journal= "", volume = "", pages = "", year = "July 2-7, 2006" } @techreport{Danieltech, author = "M. Daniel", title = "Transformations of belief functions to probabilities", institution = "Institute of Computer Science, Academy of Sciences of the Csech Republic", year = "", } @article{Haenni02ijar, author = "R. Haenni and N. Lehmann", title = "Resource bounded and anytime approximation of belief function computations", journal= "International Journal of Approximate Reasoning", volume = "31(1-2)", pages = "103-154", year = "October 2002" } @article{Denoeux02ijar, author = "T. Denoeux and A. Ben Yaghlane", title = "Approximating the Combination of Belief Functions using the Fast Moebius Transform in a coarsened frame", journal= "International Journal of Approximate Reasoning", volume = "31(1-2)", pages = "77-101", year = "October 2002" } @article{Denoeux01ijufk, author = "T. Denoeux", title = "Inner and outer approximation of belief structures using a hierarchical clustering approach", journal= "Int. Journal of Uncertainty, Fuzziness and Knowledge-Based Systems", volume = "9(4)", pages = "437-460", year = "2001" } @article{Cobb03isf, author = "B. R. Cobb and P. P. Shenoy", title = "A comparison of Bayesian and belief function reasoning", journal= "Information Systems Frontiers", volume = "5(4)", pages = "345-358", year = "2003" } @inproceedings{Cobb03ecsqaru, author = "B. R. Cobb and P. P. Shenoy", title = "A comparison of methods for transforming belief function models to probability models", booktitle= "Proceedings of ECSQARU'2003, Aalborg, Denmark", editor = "", journal= "", volume = "", pages = "255-266", year = "July 2003" } @inproceedings{Yaghlane01ecsqaru, author = "A. Ben Yaghlane and T. Denoeux and K. Mellouli", title = "Coarsening approximations of belief functions", booktitle= "Proceedings of ECSQARU'2001", editor = "S. Benferhat and P. Besnard", journal= "LNAI 2143", volume = "", pages = "362-373", year = "2001" } @article{cuzzolin05proapprox, author = "F. Cuzzolin", title = "Probabilistic approximations of belief functions", journal= "in preparation", volume = "", pages = "", year = "2005" } @inproceedings{cuzzolin05isipta, author = "F. Cuzzolin and R. Frezza", title = "Evidential modeling for pose estimation", booktitle= "Proceedings of the $4^{rd}$ Internation Symposium on Imprecise Probabilities and Their Applications (ISIPTA'05)", editor = "", journal= "", volume = "", pages = "", year = "Pittsburgh, July 2005" } @inproceedings{cuzzolin03isipta, author = "F. Cuzzolin", title = "Geometry of Upper Probabilities", booktitle= "Proceedings of the $3^{rd}$ Internation Symposium on Imprecise Probabilities and Their Applications (ISIPTA'03)", editor = "", journal= "", volume = "", pages = "", year = "July 2003" } @techreport{cobb03on, author = "B.R. Cobb and P.P. Shenoy", title = "On transforming belief function models to probability models", institution = "University of Kansas, School of Business, Working Paper No. 293", year = "February 2003", } @incollection{black97geometric, author = "P. Black", title = "Geometric Structure of Lower Probabilities", booktitle= "Random Sets: Theory and Applications", editor = "Goutsias and Malher and Nguyen", pages = "361-383", publisher= "Springer", year = "1997" } @incollection{seidenfeld97some, author = "T. Seidenfeld", title = "Some static and dynamic aspects of rubust {B}ayesian theory", booktitle= "Random Sets: Theory and Applications", editor = "Goutsias and Malher and Nguyen", pages = "385-406", publisher= "Springer", year = "1997" } @PHDTHESIS{black96examination, author = "P. Black", title = "An examination of belief functions and other monotone capacities", school = "Department of Statistics, Carnegie Mellon University", type = "{PhD} Dissertation", address = "", month = "", year = 1996, note = "Pgh. PA 15213", } @article{cuzzolin04smcb, author = "F. Cuzzolin", title = "Geometry of {D}empster's rule of combination", journal= "IEEE Transactions on Systems, Man and Cybernetics part B", volume = "34:2", pages = "961--977", year = "2004" } @book{dubois88possibility, author = "D. Dubois and H. Prade", title = "Possibility theory", publisher= "Plenum Press", address= "New York", year = "1988" } @book{klir95book, author = "G. J. Klir and B. Yuan", title = "Fuzzy sets and fuzzy logic: theory and applications", publisher= "Prentice Hall PTR", address= "Upper Saddle River, NJ", year = "1995" } @inproceedings{cuzzolin02fsdk, author = "F. Cuzzolin", title = "Geometry of {D}empster's rule", booktitle= "Proceedings of FSDK02", editor = "", journal= "", volume = "", pages = "", year = "Singapore, 18-22 November 2002" } @article{cuzzolin05smcc, author = "F. Cuzzolin", title = "Geometrical structure of belief space and conditional subspaces", journal = "submitted to the IEEE Transactions on Systems, Man and Cybernetics part C", volume = "", pages = "", year = "July 2005" } % --------------------- september 2007 @techreport{cuzzolin07report, author = "F. Cuzzolin", title = "Relative plausibility, affine combination, and {D}empster's rule", institution = "INRIA Rhone-Alpes", year = "2007", } @inproceedings{daniel04ipmu, author = {M. Daniel}, title = {Consistency of Probabilistic Transformations of Belief Functions}, booktitle = {IPMU}, year = {2004}, pages = {1135-1142} } @article{smets93dis, author = "Ph. Smets", title = "Belief functions: the disjunctive rule of combination and the generalized {B}ayesian theorem", journal= "International Journal of Approximate reasoning", volume = "9", pages = "1--35", year = "1993" } @article{daniel06on, author = "M. Daniel", title = "On Transformations of Belief Functions to Probabilities", journal= "International Journal of Intelligent Systems, special issue on Uncertainty Processing", editor = "Radim Jirouek and Gernot D. Kleiter and Jiina Vejnarová", volume = "21", number = "3", pages = "261--282", year = "February 2006" } @article{Chateauneuf89, author = "A. Chateauneuf and J.Y. Jaffray", title = "Some characterization of lower probabilities and other monotone capacities through the use of {M}öbius inversion", journal= "Math. Soc. Sci.", volume = "17", pages = "263-283", year = "1989" } @INPROCEEDINGS{ubf, AUTHOR = "Ph. Smets ", TITLE = "The Nature of the Unnormalized Beliefs Encountered in the Transferable Belief Model", BOOKTITLE = "Proceedings of the 8th Annual Conference on Uncertainty in Artificial Intelligence (UAI-92)", PUBLISHER = "Morgan Kaufmann", ADDRESS = "San Mateo, CA", YEAR = "1992", PAGES = "292-29" } @misc{ zaffalon-treebased, author = "M. Zaffalon and E. Fagiuoli", title = "Tree-Based Credal Networks for Classification", url = "citeseer.ist.psu.edu/579709.html" } @book{halpern03book, author = "J.Y. Halpern", title = "Reasoning About Uncertainty", publisher= "MIT Press", address= "", year = "2003" } @book{walley91book, author = "P. Walley", title = "Statistical Reasoning with Imprecise Probabilities", publisher= "Chapman and Hall", address= "New York", year = "1991" } @book{shafer01book, author = "Glenn Shafer and Vladimir Vovk", title = "Probability and Finance: It's Only a Game!", publisher= "Wiley", address= "New York", year = "2001" } @inproceedings{cuzzolin05hawaii, author = "F. Cuzzolin", title = "On the properties of relative plausibilities", booktitle= "Proceedings of the International Conference of the IEEE Systems, Man, and Cybernetics Society (SMC'05), Hawaii, USA" editor = "", journal= "", volume = "", pages = "", year = "October 10-12, 2005" } @inproceedings{cuzzolin04ipmu, author = "F. Cuzzolin", title = "Simplicial complexes of finite fuzzy sets", booktitle= "Proceedings of the $10^{th}$ International Conference on Information Processing and Management of Uncertainty IPMU'04, Perugia, Italy", editor = "", journal= "", volume = "", pages = "1733-1740", year = "July 4-9, 2004" } @inproceedings{cuzzolin06ipmu, author = "F. Cuzzolin", title = "The geometry of relative plausibilities", booktitle = "Proceedings of the $11^{th}$ International Conference on Information Processing and Management of Uncertainty IPMU'04, special session on ``Fuzzy measures and integrals, capacities and games", Paris, France", editor = "", journal= "", volume = "", pages = "", year = "July 2-7, 2006" } @techreport{Danieltech, author = "M. Daniel", title = "Transformations of belief functions to probabilities", institution = "Institute of Computer Science, Academy of Sciences of the Csech Republic", year = "", } @article{Haenni02ijar, author = "R. Haenni and N. Lehmann", title = "Resource bounded and anytime approximation of belief function computations", journal= "International Journal of Approximate Reasoning", volume = "31", number = "1-2", pages = "103-154", year = "October 2002" } @article{Denoeux02ijar, author = "T. Denoeux and A. Ben Yaghlane", title = "Approximating the Combination of Belief Functions using the {F}ast {M}oebius {T}ransform in a coarsened frame", journal= "International Journal of Approximate Reasoning", volume = "31", number = "1-2", pages = "77--101", year = "October 2002" } @article{Denoeux01ijufk, author = "T. Denoeux", title = "Inner and outer approximation of belief structures using a hierarchical clustering approach", journal= "Int. Journal of Uncertainty, Fuzziness and Knowledge-Based Systems", volume = "9", number = "4", pages = "437--460", year = "2001" } @article{Cobb03isf, author = "B.R. Cobb and P.P. Shenoy", title = "A comparison of {B}ayesian and belief function reasoning", journal= "Information Systems Frontiers", volume = "5", number = "4", pages = "345--358", year = "2003" } @inproceedings{Cobb03ecsqaru, author = "B. R. Cobb and P. P. Shenoy", title = "A comparison of methods for transforming belief function models to probability models", booktitle= "Proceedings of ECSQARU'2003, Aalborg, Denmark", editor = "", journal= "", volume = "", pages = "255-266", year = "July 2003" } @inproceedings{Yaghlane01ecsqaru, author = "A. Ben Yaghlane and T. Denoeux and K. Mellouli", title = "Coarsening approximations of belief functions", booktitle= "Proceedings of ECSQARU'2001", editor = "S. Benferhat and P. Besnard", journal= "LNAI 2143", volume = "", pages = "362-373", year = "2001" } @article{cuzzolin07smcb, author = "F. Cuzzolin", title = "Two new {B}ayesian approximations of belief functions based on convex geometry", journal= "IEEE Transactions on Systems, Man, and Cybernetics - Part B", volume = "37", number = "4", pages = "", year = "August 2007" } @article{cuzzolin07smcc, author = "F. Cuzzolin", title = "A geometric approach to the theory of evidence", journal = "IEEE Transactions on Systems, Man and Cybernetics part C", volume = "", pages = "", year = "2007 (to appear)" } @article{cuzzolin05proapprox, author = "F. Cuzzolin", title = "Probabilistic approximations of belief functions", journal= "in preparation", volume = "", pages = "", year = "2005" } @inproceedings{cuzzolin03isipta, author = "Fabio Cuzzolin", title = "Geometry of upper probabilities", booktitle= "Proceedings of the $3^{rd}$ Internation Symposium on Imprecise Probabilities and Their Applications (ISIPTA'03)", editor = "", journal= "", volume = "", pages = "", year = "July 2003" } @techreport{cobb03on, author = "B.R. Cobb and P.P. Shenoy", title = "On transforming belief function models to probability models", institution = "University of Kansas, School of Business, Working Paper No. 293", year = "February 2003", } @article{cobb06ijar, author = "B. Cobb and P.P. Shenoy", title = "On the plausibility transformation method for translating belief function models to probability models", journal= "Int. J. Approx. Reasoning", volume = "41", number = "3", pages = "314--330", year = "2006" } @incollection{black97geometric, author = "P. Black", title = "Geometric Structure of Lower Probabilities", booktitle= "Random Sets: Theory and Applications", editor = "Goutsias and Malher and Nguyen", pages = "361-383", publisher= "Springer", year = "1997" } @incollection{seidenfeld97some, author = "T. Seidenfeld", title = "Some static and dynamic aspects of rubust {B}ayesian theory", booktitle= "Random Sets: Theory and Applications", editor = "Goutsias and Malher and Nguyen", pages = "385-406", publisher= "Springer", year = "1997" } @PHDTHESIS{black96examination, author = "P. Black", title = "An examination of belief functions and other monotone capacities", school = "Department of Statistics, Carnegie Mellon University", type = "{PhD} Dissertation", address = "", month = "", year = 1996, note = "Pgh. PA 15213", } @article{cuzzolin04smcb, author = "F. Cuzzolin", title = "Geometry of {D}empster's rule of combination", journal= "IEEE Transactions on Systems, Man and Cybernetics part B", volume = "34", number = "2", pages = "961--977", year = "April 2004" } @article{cuzzolin06ijufks, author = "F. Cuzzolin", title = "Geometry and combinatorics of plausibility and commonality functions", journal= "submitted to the International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems", volume = "", pages = "", year = "December 2006" } @book{dubois88possibility, author = "D. Dubois and H. Prade", title = "Possibility theory", publisher= "Plenum Press", address= "New York", year = "1988" } @book{klir95book, author = "G. J. Klir and B. Yuan", title = "Fuzzy sets and fuzzy logic: theory and applications", publisher= "Prentice Hall PTR", address= "Upper Saddle River, NJ", year = "1995" } @inproceedings{cuzzolin02fsdk, author = "F. Cuzzolin", title = "Geometry of {D}empster's rule", booktitle= "Proceedings of FSDK02", editor = "", journal= "", volume = "", pages = "", year = "Singapore, 18-22 November 2002" } @book{Aigner, author = "Martin Aigner", title = "Combinatorial Theory", publisher= "Classics in Mathematics, Springer", address= "New York", year = "1979" } @PHDTHESIS{cuzzolin01thesis, author = "F. Cuzzolin", title = "Visions of a generalized probability theory", school = "Universit\`a di Padova", type = "{PhD} Dissertation", address = "Dipartimento di Elettronica e Informatica", month = "19 February ", year = 2001, note = "", } @article{kyburg87bayesian, author = "H. Kyburg", title = "Bayesian and non-{B}ayesian evidential updating", journal= "Artificial Intelligence", volume = "31:3", pages = "271-294", year = "1987" } @inproceedings{Ha, author = "V. Ha and P. Haddawy", title = "Theoretical foundations for abstraction-based probabilistic planning", booktitle= "Proc. of the $12^{th}$ Conference on Uncertainty in Artificial Intelligence", editor = "", journal= "", volume = "", pages = "291-298", year = "August 1996" } % -------------------------- old stuff @inproceedings{Doucet, author = "N. Bergman and A. Doucet ", title = "Markov Chain Monte Carlo Data Association for Target Tracking", booktitle= "IEEE Int. Conference on Acoustics, Speech and Signal Processing", volume = "", pages = "", year = "2000" } @TECHREPORT{DaveyDefence, AUTHOR = "S.J. Davey and S.B. Colgrove ", TITLE = "A Unified Probabilistic Data Assotiation Filter with Multiple Models", INSTITUTION = "Surveillance System Division, Electonic and Surveillance Reserach Lab.", YEAR = "2001", type = "", number = "DSTO-TR-1184", address = "", month = "", note = "", abstract = "", keywords = "", source = "" } @article{Dryden91, author = "I. Dryden and K.V. Mardia", title = "General Shape Distributions in a Plane", journal= "Adv. Appl. Prob.", volume = "23", pages = "259:276", year = "1991" } @inproceedings{Karlsson01, author = "R. Karlsoon and F. Gustafsson", title = "Monte Carlo data association for multiple target tracking", booktitle= "IEEE Workshop on Target Tracking", volume = "", pages = "", year = "2001" } @article{Kendall89, author = "D.G. Kendall", title = "A Survey of the Statistical Theroy of Shape", journal= "Statistical Science", volume = "4(2)", pages = "87-120", year = "1989" } @inproceedings{HagerCVPR98, author = "C. Rasmussen and G.D. Hager", title = "Joint Probabilistic Techniques for Tracking Multi-Part Objects", booktitle= "Int. Conf. on Computer Vision and Pattern Recognition", volume = "", pages = "", year = "1998" } @article{HagerPAMI2001, author = "C. Rasmussen and G.D. Hager", title = "Probabilistic Data Association Methods for Tracking Complex Visual Objects", journal = "IEEE Transaction on Patter Analysis and Machine Intelligence", volume = "23", pages = "560-576", year = "2001" } @article{cuzzolin02smc, author = "F. Cuzzolin", title = "Geometry of {D}empster's rule of combination", journal= "submitted to the IEEE Transactions on Systems, Man and Cybernetics B", volume = "", pages = "", year = "August 2002" } @inproceedings{PeronaICCV99, author = "Y. Song and L. Goncaves and E. Di Bernardo and P. Perona", title = "Monocular Perception of Biological Motion - Detection and Labelling", booktitle= "Int. Conf. on Computer Vision", volume = "", pages = "805-812", year = "1999" } @book{Lju83, author = "L. Ljung and T. Söderström", title = "Theory and practice of recursive Identification", publisher= "MIT Press", address= "", year = "1983" } @article{cuzzolin02proapprox, author = "F. Cuzzolin", title = "Probabilistic approximations of belief functions", journal= "in preparation", volume = "", pages = "", year = "" } @article{cuzzolin02posapprox, author = "F. Cuzzolin", title = "Possibilistic approximations of belief functions", journal= "submitted to the IEEE Transactions on Fuzzy Systems", volume = "", pages = "", year = "October 2002" } @article{cuzzolin02geofuzzy, author = "F. Cuzzolin", title = "Geometry of fuzzy sets", journal= "submitted to the IEEE Transactions on Fuzzy Systems", volume = "", pages = "", year = "October 2002" } @book{dubois88possibility, author = "D. Dubois and H. Prade", title = "Possibility theory", publisher= "Plenum Press", address= "New York", year = "1988" } @book{klir95book, author = "G. J. Klir and B. Yuan", title = "Fuzzy sets and fuzzy logic: theory and applications", publisher= "Prentice Hall PTR", address= "Upper Saddle River, NJ", year = "1995" } @inproceedings{cuzzolin02fsdk, author = "F. Cuzzolin", title = "Geometry of {D}empster's rule", booktitle= "Proceedings of FSDK02", editor = "", journal= "", volume = "", pages = "", year = "Singapore, 18-22 November 2002" } @article{cuzzolin02space, author = "F. Cuzzolin", title = "Geometrical structure of belief space and conditional subspaces", journal = "submitted to the IEEE Transactions on Systems, Man and Cybernetics part C", volume = "", pages = "", year = "November 2002" } @article{Cuzzolin02cano, author = "F. Cuzzolin", title = "Canonical decomposition of belief functions in the belief space", journal = "in preparation", volume = "", pages = "", year = "2002" } @book{Aigner, author = "Martin Aigner", title = "Combinatorial Theory", publisher= "Classics in Mathematics, Springer", address= "New York", year = "1979" } @PHDTHESIS{cuzzolin01thesis, author = "F. Cuzzolin", title = "Visions of a generalized probability theory", school = "Universit\`a di Padova", type = "{PhD} Dissertation", address = "Dipartimento di Elettronica e Informatica", month = "19 February ", year = 2001, note = "", } @article{kyburg87bayesian, author = "H. Kyburg", title = "Bayesian and non-{B}ayesian evidential updating", journal= "Artificial Intelligence", volume = "31:3", pages = "271-294", year = "1987" } @inproceedings{Ha, author = "V. Ha and P. Haddawy", title = "Theoretical foundations for abstraction-based probabilistic planning", booktitle= "Proc. of the $12^{th}$ Conference on Uncertainty in Artificial Intelligence", editor = "", journal= "", volume = "", pages = "291-298", year = "August 1996" } % lattices @article{Birkhoff35, author = "G. Birkhoff", title = "Abstract linear dependence and lattices", journal = "American Journal of Mathematics", volume = "57", pages = "800-804", year = "1935" } @article{Whitney35, author = "H. Whitney", title = "On the abstract properties of linear dependence", journal = "American Journal of Mathematics", volume = "57", pages = "509-533", year = "1935" } @book{Birkhoff67, author = "G. Birkhoff", title = "Lattice theory ($3^{rd}$ edition)", publisher= "Amer. Math. Soc. Colloquium Publications, Vol. 25", address= "Providence, RI", year = "1967" } % object detection @inproceedings{Perona1, author = "M. Weber and M. Welling and P. Perona", title = "Unsupervised learning of models for recognition", booktitle= "Proc. of the 6th European Conference on Computer Vision", editor = "", journal= "", volume = "1", pages = "18-32", year = "June/July 2000" } % KL distance @article{ streit, author = "R. L. Streit", title = "The Moments of Matched and Mismatched Hidden {M}arkov Models", journal = "IEEE Trans. on Acoustics, Speech, and Signal Processing", volume = "Vol. 38(4)", pages = "610-622", year = "April 1990" } @PhDTHESIS{karan, author = "M. Karan", title = "Frequency Tracking and Hidden {M}arkov Models", text = "M. Karan, Frequency Tracking and Hidden Markov Models, PhD thesis, The Australian National University, March 1995", year = "1995" } @article{ rabiner, author = "B. H. Juang and L. R. Rabiner", title = "A Probabilistic Distance Measure for Hidden {M}arkov Models", journal = "AT\&T Technical Journal", volume = "Vol. 64(2)", pages = "391-408", year = "February 1985" } % other @inproceedings{black2, author = "M. J. Black", title = "Explaining optical flow events with parameterized spatio-temporal models", booktitle = "Proc. of Conference on Computer Vision and Pattern Recognition", editor = "", journal= "", volume = "1", pages = "326-332", year = "1999" } @inproceedings{black, author = "Y. Yacoob and M. J. Black", title = "Parameterized modeling and recognition of activities", booktitle = "Computer Vision and Image Understanding", editor = "", journal= "", volume = "73(2)", pages = "232-247", year = "1999" } @book{wertheimer, author = "M. Wertheimer", title = "Laws of organization in perceptual forms", publisher= "W. D. Ellis, editor, A Sourcebook of Gestalt Psychology, pages 331--363. Harcourt, Brace and Company", address= "", year = "1939" } @inproceedings{barronFB92, author = "J. L. Barron and D. J. Fleet and S. S. Beauchemin", title = "Performance of optical flow techniques", booktitle = "International Journal of Computer Vision", editor = "", journal= "", volume = "12(1)", pages = "43-77", year = "1994" } @inproceedings{PNF, author = "C. S. Pinhanez and A. F. Bobick", title = "Human action detection using PNF propagation of temporal constraints", booktitle = "Proc. of the Conference on Computer Vision and Pattern Recognition", editor = "", journal= "", volume = "", pages = "898-904", year = "1998" } @inproceedings{essa, author = "D. Moore and I. Essa and M. Hayes III", title = "Exploiting Human Actions and Object Context for Recognition Tasks", booktitle= "Proc. of the International Conference on Computer Vision", editor = "", journal= "", volume = "1", pages = "80-86", year = "1999" } @inproceedings{mada, author = "A. Madabhushi and J. K. Aggarwal", title = "A {B}ayesian approach to human activity recognition", booktitle= "Proc. of the 2nd International Workshop on Visual Surveillance", editor = "", journal= "", volume = "", pages = "25-30", year = "June 1999" } @inproceedings{binder, author = "J. Binder and D. Koeller and S. Russell and K. Kanazawa", title = "Adaptive probabilistic networks with hidden variables", booktitle= "Machine Learning", editor = "", journal= "", volume = "29", pages = "213-244", year = "1997" } @inproceedings{brand, author = "M. Brand and N. Oliver and A. Pentland", title = "Coupled HMM for complex action recognition", booktitle = "Proc. of Conference on Computer Vision and Pattern Recognition", editor = "", journal= "", volume = "29", pages = "213-244", year = "1997" } @inproceedings{starner, author = "T. Starner and A. Pentland", title = "Real-time american sign language recognition from video using HMM", booktitle = "Proc. of ISCV 95", editor = "", journal= "", volume = "29", pages = "213-244", year = "1997" } @inproceedings{essaface, author = "I. A. Essa and A. O. Pentland", title = "Facial expression recognition using a dynamic model and motion energy", booktitle = "Proc. of the 5th Conference on Computer Vision", editor = "", journal= "", volume = "", pages = "360-367", year = "1995" } @inproceedings{blackface, author = "M. Black and P. Anandan", title = "The robust estimation of multiple motions: parametric and piecewise smooth flow fields", booktitle = "Computer Vision and Image Understanding", editor = "", journal= "", volume = "63(1)", pages = "75-104", year = "January 1996" } @inproceedings{donato, author = "G. Donato et al.", title = "Classifying facial actions", booktitle = "IEEE Journal on Pattern Analysis and Machine Intelligence", editor = "", journal= "", volume = "21(10)", pages = "974-989", year = "October 1999" } @inproceedings{gavrila, author = "D. M. Gavrila", title = "The visual analysis of human movement: A survey", booktitle = "Computer Vision and Image Understanding", editor = "", journal= "", volume = "73", pages = "82-98", year = "1999" } @inproceedings{ivanov, author = "Y. A. Ivanov and A. F. Bobick", title = "Recognition of visual activities and interactions by stochastic parsing", booktitle = "IEEE Trans. on Pattern Analysis and Machine Intelligence", editor = "", journal= "", volume = "22(8)", pages = "852-872", year = "2000" } @inproceedings{intille, author = "S. S. Intille and A. F. Bobick", title = "Visual recognition of multi agent action using binary temporal relations", booktitle = "Proc. of the Conf. on Computer Vision and Pattern Recognition", editor = "", journal= "", volume = "1", pages = "56-62", year = "1999" } @inproceedings{hoey, author = "J. Hoey and J. J. Little", title = "Representation and recognition of Complex Human Motion", booktitle = "Proc. of the Conference on Computer Vision and Pattern Recognition", editor = "", journal= "", volume = "1", pages = "752-759", year = "2000" } @inproceedings{perona, author = "M. Weber and M. Welling and P. Perona", title = "Unsupervised learning of models for recognition", booktitle= "Proc. of the 6th European Conference on Computer Vision", editor = "", journal= "", volume = "1", pages = "18-32", year = "June/July 2000" } @inproceedings{wu, author = "J. S. Liu and Y. Wu", title = "Parameter expansion for data augmentation", booktitle= "Journal of the American Statistical Association", editor = "", journal= "", volume = "94", pages = "1264-1274", year = "1999" } @inproceedings{poggio, author = "M. A. Giese and T. Poggio", title = "Morphable models for the analysis and synthesis of complex motion patterns", booktitle= "International Journal of Computer Vision", editor = "", journal= "", volume = "38(1)", pages = "1264-1274", year = "2000" } @inproceedings{bregler, author = "C. Bregler", title = "Learning and recognizing human dynamics in video sequences", booktitle= "Proc. of the Conference on Computer Vision and Pattern Recognition", editor = "", journal= "", volume = "", pages = "568-574", year = "1997" } @techreport{wilsononline, author = "A. D. Wilson and A. F. Bobick", title = "Realtime Online Adaptive Gesture Recognition", institution = "M.I.T. Media Laboratory, Tech. Rep. No. 505", year = "1999", } @inproceedings{wilsonparam, author = "A. D. Wilson and A. F. Bobick", title = "Parametric Hidden {M}arkov Models for gesture recognition", booktitle = "IEEE Trans. on Pattern Analysis and Machine Intelligence", editor = "", journal= "", volume = "21(9)", pages = "884-900", year = "Sept. 1999" } %% works of mine @inproceedings{Cuzzolin97, author = "Andrea Sorrentino and Fabio Cuzzolin and Ruggero Frezza", title = "Using Hidden {M}arkov Models and Dynamic Size Functions for Gesture Recognition", booktitle= "Proceedings of the 8th British Machine Vision Conference (BMVC97)", editor = "Adrian F. Clark", journal= "", volume = "2", pages = "560-570", year = "September 1997" } @inproceedings{Cuzzolin99, author = "Fabio Cuzzolin and Ruggero Frezza", title = "An Evidential Reasoning Framework for Object Tracking", booktitle= "SPIE - Photonics East 99 - Telemanipulator and Telepresence Technologies VI", editor = "Matthew R. Stein", journal= "", volume = "3840", pages = "13-24", year = "19-22 September 1999" } @inproceedings{Cuzzolin2000, author = "Fabio Cuzzolin and Ruggero Frezza", title = "Integrating feature spaces for object tracking", booktitle= "Proc. of the International Symposium on the Mathematical Theory of Networks and Systems (MTNS2000)", editor = "", journal= "", volume = "", pages = "", year = "21-25 June 2000" } @inproceedings{Cuzzolin2000d, author = "Fabio Cuzzolin", title = "Families of compatible frames of discernment as semimodular lattices", booktitle= "Proc. of the International Conference of the Royal Statistical Society (RSS2000)", editor = "", journal= "", volume = "", pages = "", year = "September 2000" } @inproceedings{Cuzzolin2000e, author = "Fabio Cuzzolin and Ruggero Frezza", title = "Sequences of belief functions and model-based data association", booktitle= "submitted to the IAPR Workshop on Machine Vision Applications (MVA2000)", editor = "", journal= "", volume = "", pages = "", year = "November 28-30, 2000" } @inproceedings{Cuzzolin2001, author = "Fabio Cuzzolin and Alessandro Bissacco and Ruggero Frezza and Stefano Soatto", title = "Towards Unsupervised Detection of Actions in Clutter", booktitle= "submitted to the International Conference on Computer Vision (ICCV2001)", editor = "", journal= "", volume = "", pages = "", year = "June 2001" } @inproceedings{Cuzzolin2001d, author = "Fabio Cuzzolin and Ruggero Frezza", title = "Lattice structure of the families of compatible frames", booktitle= "Proceedings of the $2^{nd}$ International Symposium on Imprecise Probabilities and their Applications (ISIPTA2001)", editor = "", journal= "", volume = "", pages = "", year = "26-29 June 2001" } @inproceedings{Cuzzolin2001e, author = "Fabio Cuzzolin and Ruggero Frezza", title = "Geometric analysis of belief space and conditional subspaces", booktitle= "Proceedings of the $2^{nd}$ International Symposium on Imprecise Probabilities and their Applications (ISIPTA2001)", editor = "", journal= "", volume = "", pages = "", year = "26-29 June 2001" } @inproceedings{cuzzolin03isipta, author = "Fabio Cuzzolin", title = "Geometry of Upper Probabilities", booktitle= "submitted to the $3^{rd}$ Internation Symposium on Imprecise Probabilities and Their Applications (ISIPTA'03)", editor = "", journal= "", volume = "", pages = "", year = "" } %% mathematical references @book{Oxley, author = "James G. Oxley", title = "Matroid theory", publisher= "Oxford University Press", address= "Great Clarendon Street, Oxford, UK", year = "1992" } @book{Farina, author = "Sergio Rinaldi and Lorenzo Farina", title = "I sistemi lineari positivi: teoria e applicazioni", publisher= "Citt\'a Studi Edizioni", address= "", year = "" } @book{Rosenbaum, author = "Albrecht Beutelspacher and Ute Rosenbaum", title = "Projective geometry", publisher= "Cambridge University Press", address= "Cambridge", year = "1998" } @book{Jacobson, author = "Nathan Jacobson", title = "Basic Algebra {I}", publisher= "Freeman and Company", address= "New York", year = "1985" } @book{Moore95, author = "R. Elliot and L. Aggoun and J. Moore", title = "Hidden {M}arkov models: estimation and control", publisher= "", address= "", year = "1995" } @book{Sikorski, author = "Roman Sikorski", title = "Boolean algebras", publisher= "Springer Verlag", address= "", year = "1964" } @book{Szasz, author = "Gabor Szasz", title = "Introduction to lattice theory", publisher= "Academic Press", address= "New York and London", year = "1963" } @book{Stern, author = "Manfred Stern", title = "Semimodular lattices", publisher= "Cambridge University Press", address= "", year = "1999" } @book{Rosenthal, author = "Kimmo I Rosenthal", title = "Quantales and their applications", publisher= "Longman scientific and technical", address= "Longman house, Burnt Mill, Harlow, Essex, UK", year = "1990" } @book{Novikov, author = "B.A. Dubrovin and S.P. Novikov and A.T. Fomenko", title = "Geometria Contemporanea 3", publisher= "Editori Riuniti", address= "", year = "1989" } @book{Novikov_russian, author = "B.A. Dubrovin and S.P. Novikov and A.T. Fomenko", title = "Sovremennaja geometrija. Metody i prilozenija", publisher= "Nauka", address= "Moscow", year = "1986" } @techreport{Socolovsky94, author = "H. Garcia-Compe\'an and J.M. L\'opez-Romero and M.A. Rodriguez-Segura and M. Socolovsky", title = "Principal bundles, connections and {BRST} cohomology", institution = "Los Alamos National Laboratory, hep-th/9408003", year = "July 1994", } %% object tracking and gesture recognition @techreport{Kanade93, author = "James M. Rehg and Takeo Kanade", title = "DigitEyes: Vision-Based Human Hand Tracking", institution = "School of Computer Science, Carnegie Mellon University, CMU-CS-93-220", year = "December 1993", } @techreport{Kanade94, author = "James M. Rehg and Takeo Kanade", title = "Visual Tracking of Self-Occluding Articulated Objects", institution = "School of Computer Science, Carnegie Mellon University, CMU-CS-94-224", year = "December 1994", } @inproceedings{Bobick95, author = "Aaron F. Bobick and Andrew D. Wilson", title = "Learning Visual Behavior for Gesture Analysis", booktitle= "IEEE Symposium on Computer Vision", editor = "", journal= "", volume = "", pages = "", year = "November 1995" } %% shape representation @inproceedings{Frosini91, author = "Patrizio Frosini", title = "Measuring Shape by Size Functions", booktitle= "Proceedings of SPIE on Intelligent Robotic Systems", editor = "", journal= "", volume = "1607", pages = "122-133", year = "1991" } %% data association @book{Shalom88, author = "Yaakov Bar-Shalom and Thomas E. Fortmann", title = "Tracking and Data Association", publisher= "Academic Press, Inc.", address= "", year = "1988" } @inproceedings{Blake96, author = "Michael Isard and Andrew Blake", title = "Contour tracking by stochastic propagation of conditional density", booktitle= "Proceedings of the European Conference of Computer Vision (ECCV96)", editor = "", journal= "", volume = "", pages = "343-356", year = "1996" } @inproceedings{Bloem95, author = "Edwin A. Bloem and Henk A.P. Blom", title = "Joint probabilistic data association methods avoiding track coalescence", booktitle= "Proceedings of the 34th Conference on Decision and Control", editor = "", journal= "", volume = "", pages = "", year = "December 1995" } % other vision applications @article{Thrun, author = "Sebastian Thrun and Wolfgang Burgard and Dieter Fox", title = "A probabilistic approach to concurrent mapping and localization for mobile robots", journal= "Autonomous Robots", volume = "5", pages = "253-271", year = "1998" } @techreport{Rao, author = "Rajesh P.N. Rao and Dana H. Ballard", title = "Dynamic model of visual recognition predicts neaural response properties in the visual cortex", institution = "Department of computer science, University of Rochester", year = "November 1995", } %% classification @book{Duda, author = "Richard O. Duda and Peter E. Hart", title = "Pattern classification and scene analysis", publisher= "John Wiley and Sons Inc.", address= "", year = "1973" } %% Theory of evidence %% books @book{Shafer76, author = "Glenn Shafer", title = "A Mathematical Theory of Evidence", publisher= "Princeton University Press", address= "", year = "1976" } @book{goutsias97random, author = "John Goutsias and Ronald P.S. Mahler and Hung T. Nguyen", title = "Random sets: theory and applications ({IMA} {V}olumes in {M}athematics and {I}ts {A}pplications, {V}ol. 97)", publisher= "Springer-Verlag", address= "", year = "December 1997" } @book{matheronrandom, author = "G. Matheron", title = "Random Sets and Integral Geometry", publisher= "Wiley Series in Probability and Mathematical Statistics", address= "", year = "" } @book{definetti74, author = "B. De Finetti", title = "Theory of Probability", publisher= "Wiley, London", address= "", year = "1974" } @book{Grabish95, author = "Michel Grabisch and Hung T. Nguyen and Elbert A. Walker", title = "Fundamentals of uncertainty calculi with applications to fuzzy inference", publisher= "Kluwer Academic Publishers", address= "", year = "1995" } @book{Walley91, author = "Peter Walley", title = "Statistical Reasoning with Imprecise Probabilities", publisher= "Chapman and Hall", address= "London", year = "1991" } @BOOK{km95book, AUTHOR = {Jurg Kohlas and Paul-Andr\'e Monney}, TITLE = {A Mathematical Theory of Hints. An Approach to {D}empster-{S}hafer Theory of Evidence}, PUBLISHER = {Springer-Verlag}, YEAR = {1995}, VOLUME = {425}, SERIES = {Lecture Notes in Economics and Mathematical Systems} } @BOOK{smithson1989, author = {M. J. Smithson}, title = {Ignorance and Uncertainty: Emerging Paradigms}, year = 1989, publisher = {Springer}, address = {New York (NY)} } @BOOK{goodman85uncertainty, author = {I. R. Goodman and Hung T. Nguyen}, title = {Uncertainty Models for Knowledge-based systems}, year = 1985, publisher = {North Holland}, address = {New York} } @BOOK{lee95fuzzy, author = {E. S. Lee and Q. Zhu}, title = {Fuzzy and Evidential Reasoning}, year = 1995, publisher = {Physica-Verlag}, address = {Heidelberg} } @BOOK{klir1988, author = {G. J. Klir and T. A. Folger}, title = {Fuzzy Sets, Uncertainty and Information}, year = 1988, publisher = {Prentice Hall}, address = {Englewood Cliffs (NJ)} } @BOOK{krause1993, author = {P. Krause and D. Clark}, title = {Representing Uncertain Knowledge}, year = 1993, publisher = {Kluwer}, address = {Dordrecht} } %% random sets and belief functions @ARTICLE{cooman1998a, author = {Gert {d}e Cooman and D. Aeyels}, title = {A random set description of a possibility measure and its natural extension}, year = {1998}, note = {submitted for publication} } @article{ross86random, author = "David Ross", title = "Random Sets Without Separability", journal= "Annals of Probability", volume = "14:3", pages = "1064-1069", year = "July 1986" } @article{Nguyen78, author = "H.T. Nguyen", title = "On Random Sets and Belief Functions", journal= "J. Mathematical Analysis and Applications", volume = "65", pages = "531-542", year = "1978" } @incollection{Nguyen97, author = "H.T. Nguyen and T. Wang", title = "Belief functions and random sets", booktitle= "Applications and Theory of Random Sets, The IMA Volumes in Mathematics and its Applications, Vol. 97", editor = "", pages = "243-255", publisher= "Springer", year = "1997" } @incollection{Hestir91, author = "H.T. Hestir and H.T. Nguyen and G.S. Rogers", title = "A random set formalism for evidential reasoning", booktitle= "Conditional Logic in Expert Systems", editor = "", pages = "309-344", publisher= "North Holland", year = "1991" } @techreport{Goutsias98, author = "John Goutsias", title = "Modeling random shapes: an introduction to random closed set theory", institution = "Department of Electrical and Computer Engineering, John Hopkins University, Baltimore, JHU/ECE 90-12", year = "April 1998", } %% fuzzy logic and belief functions @ARTICLE{dubois1987, author = {Didier Dubois and Henri Prade}, title = {The mean value of a fuzzy number}, year = 1987, journal = {Fuzzy Sets and Systems}, volume = 24, pages = { 279--300} } @article{kraetschmer98constraints, author = "Volker Kraetschmer", title = "Constraints on belief functions imposed by fuzzy random variables: Some technical remarks on Romer-Kandel", journal = "IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics", volume = "28", issue = "6", publisher = "IEEE", pages = "881-883", year = "1998", abstract="Roemer-Kandel investigated a new approach of fuzzy data analysis combining Dempster-Shafer theory and fuzzy set theory. Especially, belief measures are derived from fuzzy random variables but proved incompletely. This paper offers a completion using topological properties induced by the Hausdorff metric which is defined on the space of closed intervals of the real numbers. Moreover little corrections of some other assertions in the paper of Roemer-Kandel are presented. " } @article{heilpern97representation, author = "Stanislaw Heilpern", title = "Representation and application of fuzzy numbers", journal = "Fuzzy Sets and Systems", volume = "91", issue = "2", publisher = "Elsevier Science", pages = "259-268", year = "1997", abstract="In this paper we present the theoretical background of fuzzy numbers connected with the possibility and Dempster-Shafer theories. We describe some types of representation of fuzzy numbers and we study the notions of the distance and orders between fuzzy numbers based on these representations. The second part is devoted to the application of fuzzy numbers in data analysis, artificial intelligence and decision making." } @article{klir97constructing, author = "George J. Klir and Wang Zhenyuan and David Harmanec", title = "Constructing fuzzy measures in expert systems", journal = "Fuzzy Sets and Systems", volume = "92", issue = "2", publisher = "Elsevier Science", pages = "251-264", year = "1997", abstract="This paper is an overview of results regarding various representations of fuzzy measures and methods for constructing fuzzy measures in the context of expert systems, which were obtained by the authors and their associates during the last three years. Included are methods for constructing fuzzy measures by various transformations, by extension, by statistical inference, and by various data-driven methods based either on the Sugeno-integral or the Choquet-integral and using neural networks, genetic algorithms, or fuzzy relation equations." } @article{klir99fuzzy, author = "George J. Klir", title = "On fuzzy-set interpretation of possibility theory", journal = "Fuzzy Sets and Systems", volume = "108", issue = "3", publisher = "Elsevier Science", pages = "263-273", year = "1999", abstract="A revised fuzzy-set interpretation of possibility theory is introduced in this paper. Contrary to the standard fuzzy-set interpretation of possibility theory, which is coherent only for normal fuzzy sets, the revised interpretation is shown to be coherent for all fuzzy sets. It is also argued that the revised interpretation, which coincides with the standard one for normal fuzzy sets, is more meaningful on intuitive grounds. Prior to the introduction of the revised interpretation, previous efforts to overcome the well-known difficulties of the standard interpretation are critically examined, and it is demonstrated that none of them results in a coherent and meaningful interpretation of possibility theory." } @article{lucas99generalization, author = "Lucas Caro and Araabi Babak Nadjar", title = "Generalization of the {D}empster-{S}hafer theory: a fuzzy-valued measure", journal = "IEEE Transactions on Fuzzy Systems", volume = "7", issue = "3", publisher = "IEEE", pages = "255-270", year = "1999", abstract="The Dempster-Shafer theory (DST) may be considered as a generalization of the probability theory, which assigns mass values to the subsets of the referential set and suggests an interval-valued probability measure. There have been several attempts for fuzzy generalization of the DST by assigning mass (probability) values to the fuzzy subsets of the referential set. The interval-valued probability measures thus obtained are not equivalent to the original fuzzy body of evidence. In this paper, a new generalization of the DST is put forward that gives a fuzzy-valued definition for the belief, plausibility, and probability functions over a finite referential set. These functions are all equivalent to one another and to the original fuzzy body of evidence. The advantage of the proposed model is shown in three application examples. It can be seen that the proposed generalization is capable of modeling the uncertainties in the real world and eliminate the need for extra preassumptions and preprocessing." } @article{yager96normalization, author = "Ronald R. Yager", title = "On the Normalization of Fuzzy Belief Structures", journal = "International Journal of Approximate Reasoning", volume = "14", issue = "2-3", publisher = "Elsevier Science", pages = "127-153", year = "1996", abstract="The issue of normalization in the fuzzy Dempster-Shafer theory of evidence is investigated. We suggest a normalization procedure called smooth normalization. It is shown that this procedure is a generalization of the usual Dempster normalization procedure. We also show that the usual process of normalizing an individual subnormal fuzzy subset by proportionally increasing the membership grades until the maximum membership grade is one is a special case of this smooth normalization process and in turn closely related to the Dempster normalization process. We look an alternative normalization process in the fuzzy Dempster-Shafer environment based on adding to the membership grade of subnormal focal elements the amount by which the fuzzy subset is subnormal." } @article{yen92computing, author = "John Yen", title = "Computing Generalized Belief Functions for Continuous Fuzzy Sets", journal = "International Journal of Approximate Reasoning", volume = "6", issue = "", publisher = "", pages = "1-31", year = "1992" } @article{young98updating, author = "Virginia R. Young and Shaun S. Wang", title = "Updating non-additive measures with fuzzy information", journal = "Fuzzy Sets and Systems", volume = "94", issue = "3", publisher = "Elsevier Science", pages = "355-366", year = "1998", abstract="We present several rules for updating non-additive set functions, defined and conditioned on fuzzy sets. Among these formulas are the Dempster-Shafer rule for belief functions and the Bayes conditioning rule. We develop the update formulas in the framework of non-additive measure and integration theory; thus, we generalize the work of Denneberg (1994). We explore the properties of the update rules and relate them to measures of (weak) fuzzy subsethood and to fuzzy inference operators. Specifically, we connect the Bayes update rule with Kosko\'s measure of fuzzy subsethood and with Mamdani\'s implication operator. Also, we connect the Dempster-Shafer update rule with the weak inclusion measure of fuzzy subsethood and with a well-known implication operator." } @article{yager99class, author = "Ronald R. Yager", title = "Class of fuzzy measures generated from a {D}empster-{S}hafer belief structure", journal = "International Journal of Intelligent Systems", volume = "14", issue = "12", publisher = "John Wiley and Sons", pages = "1239-1247", year = "1999", abstract="Here the Dempster-Shafer belief structure is viewed as providing partial information about the underlying fuzzy measure associated with a uncertain variable. In this perspective there exists many possible fuzzy measures that can be associated with a Dempster-Shafer belief structure. Typically only two of these measures have been made explicit, those being the measure of belief and plausibility. Here we introduce a whole class of fuzzy measures that can be associated with a Dempster-Shafer belief structure. As an aid to choosing between these myriad of possibilities we discuss the entropy of a fuzzy measure. " } @article{mahler95combining, author = "Ronald P.S Mahler", title = "Combining ambiguous evidence with respect to ambiguous a priori knowledge. Part II: Fuzzy logic", journal = "Fuzzy Sets and Systems", volume = "75", issue = "3", publisher = "Elsevier Science", pages = "319-354", year = "1995", abstract="This paper describes fuzzy conditioned Dempster-Shafer (FCDS) theory, a probability-based calculus for dealing with possibly imprecise and vague evidence when the underlying a priori knowledge base is itself possibly imprecise and vague. FCDS has the same general form as existing fuzzy Dempster-Shafer theories. FCDS, however, employs a finite-level Zadeh fuzzy logic and a Dempster-Shafer-like combination operator which is conditioned to reflect the influence of any a priori knowledge base which can be modeled by a belief measure on finite-level fuzzy sets. We show that FCDS is grounded in probability theory-specifically, in the theory of random fuzzy sets. We also show that it is a generalization of Bayesian theory to the case when both evidence and a priori knowledge are imprecise and vague. We show that FCDS is consistent with the lattice structure of Zadeh\'s min-max fuzzy logic and that, in particular, it possesses an analog of the familiar Moebius transform." } @INCOLLECTION{feriet1982, author = {J. Kamp\'e de F\'eriet}, editor = {Gupta, M. M. and Sanchez, E.}, title = {Interpretation of membership functions of fuzzy sets in terms of plausibility and belief}, year = 1982, pages = {93--98}, booktitle = {Fuzzy Information and Decision Processes}, publisher = {North-Holland}, address = {Amsterdam} } @inproceedings{palacharla94understanding, author = "P. Palacharla and P. C. Nelson", title = "Understanding Relations between Fuzzy Logic and Evidential Reasoning Methods", booktitle= "Proceedings of Third IEEE International Conference on Fuzzy Systems", volume = 1, pages = "1933-1938", year = "1994" } @inproceedings{Renaud99, author = "Simon Petit-Renaud and Thierry Denoeux", title = " Handling different forms of uncertainty in regression analysis: a fuzzy belief structure approach", booktitle= "Proceedings of The Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty - Ecsqaru ( Lecture Notes in Computer Science Series)", editor = "", journal= "", volume = "", pages = "", year = "London, 5-9 July 1999" } %% neural networks and belief functions @article{wang98majority, author = "Chua-Chin Wang and Hon-Son Don", title = "The majority theorem of centralized multiple BAMs networks", journal = "Information Sciences", volume = "110", issue = "3-4", publisher = "Elsevier Science", pages = "179-193", year = "1998", abstract="A method for modeling the learning of belief combination in evidential reasoning using a neural network is presented. A centralized network composed of multiple bidirectional associative memories (BAMs) sharing a single output array of neurons is proposed to process the uncertainty management of many pieces of evidence simultaneously. The convergence properties of the multi-BAM network are proved. The combination process of evidence is considered as a resonant process through the multi-BAM networks. Most important of all, a majority rule of decision making in presentation of multiple evidence is also found by the study of signal-noise-ratio (SNR) of the multi-BAM network. Some simulation examples are given. The result is coherent with the intuition of reasoning." } %% hints and belief functions @book{Kohlas95, author = "Jurg Kohlas and Paul-Andr\'e Monney", title = "A Mathematical Theory of Hints - An Approach to the {D}empster-{S}hafer Theory of Evidence", publisher= "Lecture Notes in Economics and Mathematical Systems, Springer-Verlag", address= "", year = "1995" } @ARTICLE{kohlas97allocation, AUTHOR = "Jurg Kohlas", TITLE = "Allocation of Arguments and Evidence Theory", JOURNAL = "Theoretical Computer Science", YEAR = "1997", VOLUME = "171", PAGES = "221-246", URL = "http://www2-iiuf.unifr.ch/tcs/publications/ps/kohlas97b.ps.Z", ABSTRACT = "The Dempster-Shafer theory of evidence is developed here in a very general setting. First, its symbolic or algebraic part is discussed as a body of arguments which contains an allocation of support and an allowment of possibility for each hypothesis. It is shown how such bodies of arguments arise in the theory of hints and in assumption-based reasoning in logic. A rule of combination of bodies of arguments is then defined which constitutes the symbolic counterpart of Dempster's rule. Bodies of evidence are next introduced by assigning probabilities to arguments. This leads to support and plausibility functions on some measurable hypotheses. As expected in Dempster-Shafer theory, they are shown to be set functions, monotone or alternating of infinite order respectively. It is shown how these support and plausibility functions can be extended to all hypotheses. This constitutes then the numerical part of evidence theory. Finally, combination of evidence based on the combination of bodies of arguments is discussed and a generalized version of Dempster's rule is derived. The approach to evidence theory proposed is general and is not limited to finite frames." } @incollection{kohlas95modelbased, AUTHOR = "Jurg Kohlas and Paul-Andr\'e Monney and R. Haenni and N. Lehmann", TITLE = "Model-Based Diagnostics Using Hints", BOOKTITLE = "Symbolic and Quantitative Approaches to Uncertainty, European Conference ECSQARU95, Fribourg", ORGANIZATION = "Lecture Notes in Computer Science, no. 946", PUBLISHER = "Springer", YEAR = "1995", EDITOR = "Ch. Fridevaux and J. Kohlas", PAGES = "259--266", URL = "http://www2-iiuf.unifr.ch/tcs/publications/ps/kmhl95.ps.Z", ABSTRACT = "It is often possible to describe the correct functioning of a system by a mathematical model. As long as observations or measurements correspond to the predictions made by the model, the system may be assumed to be functioning correctly. When, however, a discrepancy arises between the observations and the model-based predictions, then an explanation for this fact has to be found. The foundation of this approach to diagnostics has been laid by Reiter (1987). The explanations generated by his method, called diagnoses, are not unique in general. In addition, they are not weighed by a likelihood measure which would make it possible to compare them. We propose here the theory of hints -- an interpretation of the Dempster-Shafer Theory of Evidence -- as a very natural and general method for model-based diagnostics (for an introduction to the theory of hints, see Kohlas, Monney 1995). Note that Peng, Reggia (1990) and DeKleer, Williams (1987) also discuss probabilistic approaches to diagnostic problems." } @INCOLLECTION{kohlas95foundations, AUTHOR = {Jurg Kohlas}, TITLE = {Mathematical Foundations of Evidence Theory}, BOOKTITLE = {Mathematical Models for Handling Partial Knowledge in Artificial Intelligence}, ORGANIZATION = {}, PUBLISHER = {Plenum Press}, YEAR = {1995}, EDITOR = {G. Coletti and D. Dubois and R. Scozzafava}, PAGES = {31--64}, URL = {http://www2-iiuf.unifr.ch/tcs/publications/ps/kohlas95a.ps.Z} } @INPROCEEDINGS{kohlas94representation, AUTHOR = {Jurg Kohlas and Paul-Andr\'e Monney}, TITLE = {Representation of Evidence by Hints}, BOOKTITLE = {Advances in the Dempster-Shafer Theory of Evidence}, YEAR = {1994}, EDITOR = {R.R. Yager and J. Kacprzyk and M. Fedrizzi}, PUBLISHER = {John Wiley, New York}, PAGES = {473--492}, URL = {http://www2-iiuf.unifr.ch/tcs/publications/ps/km94c.ps.Z}, ABSTRACT = {This paper introduces a mathematical model of a hint as a body of imprecise and uncertain information. Hints are used to judge hypotheses: the degree to which a hint supports a hypothesis and the degree to which a hypothesis appears as plausible in the light of a hint are defined. This leads in turn to support- and plausibility functions. Those functions are characterized as set functions which are normalized and monotone or alternating of order $\infty$. This relates the present work to G. Shafer's mathematical theory of evidence. However, whereas Shafer starts out with an axiomatic definition of belief functions, the notion of a hint is considered here as the basic element of the theory. It is shown that a hint contains more information than is conveyed by its support function alone. Also hints allow for a straightforward and logical derivation of Dempster's rule for combining independent and dependent bodies of information. This paper presents the mathematical theory of evidence for general, infinite frames of discernment from the point of view of a theory of hints.} } @TECHREPORT{kohlas94mathematical, AUTHOR = {Jurg Kohlas}, TITLE = {Mathematical Foundations of Evidence Theory}, INSTITUTION = {Institute of Informatics, University of Fribourg}, YEAR = {1994}, TYPE = {}, NUMBER = {94-09}, ADDRESS = {}, MONTH = {}, NOTE = {Lectures to be presented at the International School of Mathematics ``G. Stampacchia" Mathematical Methods for Handling Partial Knowledge in Artificial Intelligence Erice, Sicily, June 19-25, 1994}, URL = {http://www2-iiuf.unifr.ch/tcs/publications/ps/kohlas94.ps.Z}, ABSTRACT = {} } @TECHREPORT{km90, AUTHOR = {Jurg Kohlas and Paul-Andr\'e Monney}, TITLE = {Modeling and Reasoning with Hints}, INSTITUTION = {Institute for Automation and Operations Research, University of Fribourg}, YEAR = {1990}, TYPE = {}, NUMBER = {174}, ADDRESS = {}, MONTH = {}, ABSTRACT = {Summary Paper of Theory of Hints. Introduction to math. DS-Theory. to what degree a body of information supports or contradicts, proves or disproves hypothesis. The math. model of Hints. Strike on the metro example. plausibility function. Basic probability assignments. Combining hints (DS-Rule). Difference between homogeneous/ heterogeneous and conflicting hints. Property of DS Rule. Conditioning Hints. Bayesian Hints. Frames of Discernment. Multivariate Models. Combining Hints on multivariate models. Conditional Information. Bayesian Modeling. Uncertain relations. Uncertain implication. Conditional probabilities. Link between DS-Rule and Bayes Formula. Introduction of qualitative Markov-Trees, Hypertrees. Belief updating. Arithmetic of numerical Hints. Appendix: Proofs.} } %% possibilities and belief functions @article{dubois01using, author = "Didier Dubois and M. Grabisch and Henri Prade and Philippe Smets", title = "Using the transferable belief model and a qualitative possibility theory approach on an illustrative example: the assessment of the value of a candidate", journal= "Intern. J. Intell. Systems", volume = "", pages = "", year = "2001" } @article{dubois97bayesian, author = "Didier Dubois and Henri Prade", title = "Bayesian conditioning in possibility theory", journal = "Fuzzy Sets and Systems", volume = "92", issue = "2", publisher = "Elsevier Science", pages = "223-240", year = "1997", abstract="In this paper, possibility measures are viewed as upper bounds of ill-known probabilities, since a possibility distribution is a faithful encoding of a set of lower bounds of probabilities bearing on a nested collection of subsets. Two kinds of conditioning can be envisaged in this framework, namely revision and focusing. On the one hand, revision by a sure event corresponds to adding an extra constraint enforcing that this event is impossible. On the other hand, focusing amounts to a sensitivity analysis on the conditioned probability measures (induced by the lower bound constraints). When focusing on a particular situation, the generic knowledge encoded by the probability bounds is applied to this situation, without aiming at modifying the generic knowledge. It contrasts with revision where the generic knowledge is modified by the new constraint. This paper proves that focusing applied to a possibility measure yields a possibility measure again, which means that the conditioning of a family of probabilities, induced by lower bounds bearing on probabilities of nested events, can be faithfully handled on the possibility representation itself. Relationships with similar results in the belief function setting are pointed out. Lastly the application of possibilistic focusing to exception-tolerant inference is suggested." } @incollection{Shafer87c, author = "Glenn Shafer", title = "Belief functions and possibility measures", booktitle= "Analysis of Fuzzy Information 1: Mathematics and logic", editor = "Bezdek", pages = "51-84", publisher= " CRC Press", year = "1987" } %% capacities and belief functions @ARTICLE{chateauneuf1989, author = {A. Chateauneuf and J. Y. Jaffray}, title = {Some characterizations of lower probabilities and other monotone capacities through the use of {M}\"obius inversion}, year = 1989, journal = {Mathematical Social Sciences}, volume = 17, pages = {263--283} } @article{hendon96product, author = "Ebbe Hendon and Hans Jorgen Jacobsen and Birgitte Sloth and Torben Tranaes", title = "The Product of Capacities and Belief Functions", journal= "Mathematical Social Sciences", volume = "32", pages = "95-108", year = "1996" } @article{denneberg00totally, author = "Dieter Denneberg", title = "Totally monotone core and products of monotone measures", journal = "International Journal of Approximate Reasoning", volume = "24", issue = "2-3", publisher = "Elsevier Science", pages = "273-281", year = "2000", abstract="Several approaches to the product of non-additive monotone measures (or capacities) are discussed and a new approach is proposed. It starts with the Moebius product [E. Hendon, H.J. Jacobsen, B. Sloth, T. Tranaes, The product of capacities and belief functions, Mathematical Social Sciences 32 (1996) 95-108] of totally monotone measures and extends it by means of a supremum to general monotone measures. The sup runs over sets of totally monotone measures. These sets are defined like the core of monotone measures (or cooperative games). The new product is compatible with the partial order for arbitrary monotone measures." } @article{wang97choquet, author = "Zhenyuan Wang and George J. Klir", title = "Choquet Integrals and Natural Extensions of Lower Probabilities", journal = "International Journal of Approximate Reasoning", volume = "16", issue = "2", publisher = "Elsevier Science", pages = "137-147", year = "1997", abstract="Both the Choquet integral with respect to monotone set functions and the natural extensions of lower probabilities are generalizations of the Lebesgue integral with respect to «sigma»-additive measures. The relation between these generalizations is investigated. We show that the Choquet integral with respect to a belief measure is always greater than or equal to the corresponding natural extension. Also, we compare some concepts introduced in the theory of imprecise probabilities with concepts established in fuzzy measure theory, capacity theory, and Dempster-Shafer theory." } %% incidences @article{bundy85incidence, author = "A. Bundy", title = "Incidence calculus: A mechanism for probability reasoning", journal = "Journal of automated reasoning", volume = "1", issue = "", publisher = "", pages = "263-283", year = "1985" } @article{liu98method, author = "W. Liu and D. McBryan and A. Bundy", title = "Method of assigning incidences", journal = "Applied Intelligence", volume = "9", issue = "2", publisher = "Kluwer Academic Publishers", pages = "139-161", year = "1998", abstract="Incidence calculus is a probabilistic logic in which incidences, standing for the situations in which formulae may be true, are assigned to some formulae, and probabilities are assigned to incidences. However, numerical values may be assigned to formulae directly without specifying the incidences. In this paper, we propose a method of discovering incidences under these circumstances which produces a unique output comparing with the large number of outputs from other approaches. Some theoretical aspects of this method are thoroughly studied and the completeness of the result generated from it is proved. The result can be used to calculate mass functions from belief functions in the Dempster-Shafer theory of evidence (DS theory) and define probability spaces from inner measures (or lower bounds) of probabilities on the relevant prepositional language set. " } %% fundaments @article{smets83information, author = "Philippe Smets", title = "Information Content of an Evidence", journal= "International Journal of Man Machine Studies", volume = "19", pages = "33-43", year = "1983" } @article{wilson92howmuch, author = "Nic Wilson", title = "How Much Do You Believe", journal = "International Journal of Approximate Reasoning", volume = "6", issue = "", publisher = "Elsevier Science", pages = "345-365", year = "1992" } @article{provan92validity, author = "Gregory Provan", title = "The Validity of {D}empster-{S}hafer Belief Functions", journal = "International Journal of Approximate Reasoning", volume = "6", issue = "", publisher = "Elsevier Science", pages = "389-399", year = "1992" } @article{walley00towards, author = "Peter Walley", title = "Towards a unified theory of imprecise probability", journal = "International Journal of Approximate Reasoning", volume = "24", issue = "2-3", publisher = "Elsevier Science", pages = "125-148", year = "2000", abstract="Coherent upper and lower probabilities, Choquet capacities of order 2, belief functions and possibility measures are amongst the most popular mathematical models for uncertainty and partial ignorance. Examples are given to show that these models are not sufficiently general to represent some common types of uncertainty. In particular, they are not sufficiently informative about expectations and conditional probabilities. Coherent lower previsions and sets of probability measures are considerably more general, but they may not be sufficiently informative for some purposes. Two other models for uncertainty, which involve partial preference orderings and sets of desirable gambles, are discussed. These are more informative and more general than the previous models, and they may provide a suitable mathematical foundation for a unified theory of imprecise probability." } @article{smets97normative, author = "Philippe Smets", title = "The normative representation of quantified beliefs by belief functions", journal = "Artificial Intelligence", volume = "92", issue = "1-2", publisher = "Elsevier Science", pages = "229-242", year = "1997", abstract="The use of belief functions has recently been advocated as an alternative to the use of probability functions in order to represent quantified beliefs. Such a proposal lacked justification. We present a set of requirements that justify the use of belief functions. The assessment of the validity of these requirements provides a tool for assessing the relative value of normative models of subjective behaviors." } @article{joslyn98towards, author = "Cliff Joslyn and Luis Rocha", title = "Towards a formal taxonomy of hybrid uncertainty representations", journal = "Information Sciences", volume = "110", issue = "3-4", publisher = "Elsevier Science", pages = "255-277", year = "1998", abstract="In this paper we present some ideas about how to formally relate various uncertainty representations together in a taxonomic structure, capturing both syntactic and semantic generalization. Fuzziness and nonspecificity are presumed as primitive concepts of uncertainty, and transitive and intransitive methods operating with nonspecificity and fuzziness are introduced to generate a base class of hybrid uncertainty representational forms. Additive, maximal, and interval constraints then complete the characterization of the most important hybrid forms." } @article{Ruspini92, author = "E. H. Ruspini and J.D. Lowrance and T. M. Strat", title = "Understanding evidential reasoning", journal= "International Journal of Approximate Reasoning", volume = "6", pages = "401--424", year = "1992" } @ARTICLE{williams1978, author = {P. M. Williams}, title = {On a new theory of epistemic probability}, year = 1978, journal = {British Journal for the Philosophy of Science}, volume = 29, pages = {375--387} } @article{dempster82lindleys, author = "A.P. Dempster", title = "Lindley's Paradox: Comment", journal= "Journal of the American Statistical Association", volume = "77:378", pages = "339-341", year = "June 1982" } @article{Shafer81, author = "Glenn Shafer", title = "Constructive probability", journal= "Synthese", volume = "48", pages = "309-370", year = "1981" } @article{Shafer85b, author = "Glenn Shafer", title = "Conditional probability", journal= "International Statistical Review", volume = "53", pages = "261-277", year = "1985" } @article{Shafer87d, author = "Glenn Shafer", title = "Probability judgment in artificial intelligence and expert systems", journal= "Statistical Science", volume = "2", pages = "3-44", year = "1987" } @article{Shafer90, author = "Glenn Shafer", title = "Perspectives on the theory and practice of belief functions", journal= "International Journal of Approximate Reasoning", volume = "4", pages = "323-362", year = "1990" } @article{Klir90, author = "G. J. Klir and A. Ramer", title = "Uncertainty in the {D}empster-{S}hafer theory: a critical re-examination", journal= "International Journal of General Systems", volume = "18", pages = "155-166", year = "1990" } @article{Pearl90, author = "Judea Pearl", title = "Reasoning with belief functions: an analysis of compatibility", journal= "International Journal of Approximate Reasoning", volume = "4", pages = "363-389", year = "1990" } @article{pearl86hierarchy, author = "Judea Pearl", title = "On Evidential Reasoning in a Hierarchy of Hypotheses", journal= "Artificial Intelligence", volume = "28:1", pages = "9-15", year = "1986" } @article{Pearl92, author = "Judea Pearl", title = "Rejoinder to comments on `reasoning with belief functions: an analysis of compatibility'", journal= "International Journal of Approximate Reasoning", volume = "6", pages = "425-443", year = "1992" } @article{Shafer90a, author = "Glenn Shafer", title = "Perspectives on the theory and practice of belief functions", journal= "International Journal of Approximate Reasoning", volume = "4", pages = "323-36", year = "1990" } @article{Shafer92, author = "Glenn Shafer", title = "Rejoinders to comments on `perspectives on the theory and practice of belief functions'", journal= "International Journal of Approximate Reasoning", volume = "6", pages = "445-480", year = "1992" } @article{smets92resolving, author = "Philippe Smets", title = "Resolving misunderstandings about belief functions'", journal= "International Journal of Approximate Reasoning", volume = "6", pages = "321-34", year = "1992" } @article{Wasserman92, author = "L. A. Wasserman", title = "Comments on shafer's `perspectives on the theory and practice of belief functions`", journal= "International Journal of Approximate Reasoning", volume = "6", pages = "367-375", year = "1992" } @article{Dempster67, author = "A. P. Dempster", title = "Upper and lower probability inferences based on a sample from a finite univariate population", journal= "Biometrika", volume = "54", pages = "515-528", year = "1967" } @article{Walley82frequentist, author = "Peter Walley and T. L. Fine", title = "Towards a frequentist theory of upper and lower probability", journal= "The Annals of Statistics", volume = "10", pages = "741-761", year = "1982" } @article{halpern92twoviews, author = "J. Y. Halpern and R. Fagin", title = "Two views of belief: belief as generalized probability and belief as evidence", journal= "Artificial Intelligence", volume = "54", pages = "275-317", year = "1992", abstract="Belief functions are mathematical objects defined to satisfy three axioms that look somewhat similar to the Kolmogorov axioms defining probability functions. We argue that there are (at least) two useful and quite different ways of understanding belief functions. The first is as a generalized probability function (which technically corresponds to the inner measure induced by a probability function). The second is as a way of representing evidence. Evidence, in turn, can be understood as a mapping from probability functions to probability functions. It makes sense to think of updating a belief if we think of it as a generalized probability. On the other hand, it makes sense to combine two beliefs (using, say, Dempster's rule of combination) only if we think of the belief functions as representing evidence. Many previous papers have pointed out problems with the belief function approach; the claim of this paper is that these problems can be explained as a consequence of confounding these two views of belief functions." } @ARTICLE{suppes1977, author = "P. Suppes and M. Zanotti", title = "On using random relations to generate upper and lower probabilities", year = "1977", journal = "Synthese", volume = "36", pages = "427-440" } @article{Kyburg87, author = "H. E. Kyburg", title = "Bayesian and non-{B}ayesian evidential updating", journal= "Artificial Intelligence", volume = "31", pages = "271-293", year = "1987", abstract = "Four main results are arrived at in this paper. (1) Closed convex sets of classical probability functions provide a representation of belief that includes the representations provided by Shafer probability mass functions as a special case. (2) The impact of ``uncertain evidence'' can be (formally) represented by Dempster conditioning, in Shafer's framework. (3) The impact of ``uncertain evidence'' can be (formally) represented in the framework of convex sets of classical probabilities by classical conditionalization. (4) The probability intervals that result from Dempster-Shafer updating on uncertain evidence are included in (and may be properly included in) the intervals that result from Bayesian updating on uncertain evidence." } @article{blackmondlaskey89assumptions, author = "Kathryn Blackmond Laskey and Paul E. Lehner", title = "Assumptions, beliefs and probabilities", journal = "Artificial Intelligence", volume = "41", issue = "1", publisher = "Elsevier Science", pages = "65-77", year = "1989", abstract="A formal equivalence is demonstrated between Shafer-Dempster belief theory and assumption-based truth maintenance with a probability calculus on the assumptions. This equivalence means that any Shafer-Dempster inference network can be represented as a set of ATMS justifications with probabilities attached to assumptions. A proposition's belief is equal to the probability of its label conditioned on label consistency. An algorithm is given for computing these beliefs. When the ATMS is used to manage beliefs, non-independencies between nodes are automatically and correctly accounted for. The approach described here unifies symbolic and numeric approaches to uncertainty management, thus facilitating dynamic construction of quantitative belief arguments, explanation of beliefs, and resolution of conflicts." } @article{lee88comparison, author = "Chia-Hoang Lee", title = "A comparison of two evidential reasoning schemes", journal = "Artificial Intelligence", volume = "35", issue = "1", publisher = "Elsevier Science", pages = "127-134", year = "1988", abstract="Cordon and Shortliffe [2] advocate the use of Dempster-Shafer (D-S) theory in the evidence-gathering process. It is stated that they are unaware of any formal model which could allow inexact reasoning at whatever level of abstraction. Pearl [3] later shows how evidential reasoning can be conducted in the same hypothesis space using a Bayesian model. The purpose of this note is to examine the difference between these two schemes, and to point out certain inconsistencies of this Bayesian model with the motives behind the use of the D-S model." } @article{denoeux99reasoning, author = "Thierry Denoeux", title = "Reasoning with Imprecise Belief Structures", journal= "International Journal of Approximate Reasoning", volume = "20", pages = "79-111", year = "1999" } @INCOLLECTION{shafer1976a, author = {Glenn Shafer}, editor = {Harper, W. L. and Hooker, C. A.}, title = {A theory of statistical evidence}, year = 1976, volume = 2, pages = {365--436}, booktitle = {Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science}, publisher = {Reidel}, address = {Dordrecht}, note = {with discussion} } @INCOLLECTION{zadeh1986, author = {L. A. Zadeh}, editor = {Kanal, L. N. and Lemmer, J. F.}, title = {Is probability theory sufficient for dealing with uncertainty in {AI}: a negative view}, year = 1986, pages = {103--116}, booktitle = {Uncertainty in Artificial Intelligence}, publisher = {North-Holland}, volume = 2, address = {Amsterdam} } @incollection{Smets88, author = "Philippe Smets", title = "Belief functions", booktitle= "Non-Standard Logics for Automated Reasoning", editor = "Ph. Smets and A. Mamdani and D. Dubois and H. Prade", pages = "253-286", publisher= "Academic Press, London", year = "1988" } @incollection{Shafer85a, author = "Glenn Shafer", title = "Nonadditive probability", booktitle= "Encyclopedia of Statistical Sciences", editor = "Kotz and Johnson", pages = "6, 271-276", publisher= "Wiley", year = "1985" } @incollection{Levi83, author = "I. Levi", title = "Consonance, dissonance and evidentiary mechanism", booktitle= "Festschrift for Soren Hallden", editor = "", pages = "27-42", publisher= "Theoria", year = "1983" } @inproceedings{wakker99dempster, author = "Peter P. Wakker", title = "Dempster-Belief Functions Are Based on the Principle of Complete Ignorance", booktitle= "Proceedings of the 1st International Sysmposium on Imprecise Probabilites and Their Applications", editor = "", journal= "", volume = "", pages = "535-542", year = "Ghent, Belgium, 29 June - 2 July 1999" } @inproceedings{Smets97FAPR2, author = "Philippe Smets and Roger Cooke", title = "How to Derive Belief Functions Within Probabilistic Frameworks?", booktitle= "Proceedings of the International Joint Conference on Qualitative and Quantitative Practical Reasoning (ECSQARU / FAPR '97)", editor = "", journal= "", volume = "", pages = "", year = "Bad Honnef, Germany, 9-12 June 1997" } @inproceedings{Ruspini87, author = "E.H. Ruspini", title = "Epistemic logics, probability and the calculus of evidence", booktitle= "Proc. 10th Intl. Joint Conf. on AI (IJCAI-87)", editor = "", journal= "", volume = "", pages = "924-931", year = "1987" } @inproceedings{Fagin88, author = "R. Fagin and J.Y. Halpern", title = "Uncertainty, belief and probability", booktitle= "Proc. Intl. Joint Conf. in AI (IJCAI-89)", editor = "", journal= "", volume = "", pages = "1161-1167", year = "1988" } @inproceedings{Lowrance82, author = "John D. Lowrance and T. D. Garvey", title = "Evidential reasoning: A developing concept", booktitle= "Proceedings of the Internation Conference on Cybernetics and Society", editor = "Institute of Electrical and Electronical Engineers", journal= "", volume = "", pages = "6-9", year = "1982" } @inproceedings{benferhat95belief, author = "S. Benferhat and A. Saffiotti and Ph. Smets", title = "Belief functions and default reasoning", booktitle= "Procs. of the 11th Conf. on Uncertainty in AI. Montreal, Canada", editor = "", journal= "", volume = "", pages = "19-26", year = "1995" } @techreport{Walley91coherent, author = "Peter Walley", title = "Coherent lower (and upper) probabilities", institution = "University of Warwick, Coventry (U.K.), Statistics Research Report 22", year = "1981", } @techreport{kramosil97probabilistic, author = "Ivan Kramosil", title = "Probabilistic Analysis of {D}empster-{S}hafer Theory. Part One", institution = "Academy of Science of the Czech Republic, Technical Report 716", year = "1997", } @techreport{kramosil98probabilistic, author = "Ivan Kramosil", title = "Probabilistic Analysis of {D}empster-{S}hafer Theory. Part Two.", institution = "Academy of Science of the Czech Republic, Technical Report 749", year = "1998", } %% frameworks @article{an93relation, author = "Z. An and D. A. Bell and J. G. Hughes", title = "Relation-Based Evidential Reasoning", journal = "International Journal of Approximate Reasoning", volume = "8", issue = "", publisher = "", pages = "231-251", year = "1993" } @article{Kramosil96nonnumerical, author = "Ivan Kramosil", title = "Expert systems with non-numerical belief functions", journal = "Problems of control and information theory", volume = "16", issue = "1", publisher = "Elsevier Science", pages = "39-53", year = "1996" } @article{wierzchon97modified, author = "S.T. Wierzchon and M.A. Klopotek", title = "Modified component valuations in valuation based systems as a way to optimize query processing", journal = "Journal of Intelligent Information Systems", volume = "9", issue = "2", publisher = "Kluwer Academic Publishers", pages = "157-180", year = "1997", abstract="Valuation-Based System (VBS for short) can represent knowledge in different domains including probability theory, Dempster-Shafer theory and possibility theory. More recent studies show that the framework of VBS is also appropriate for representing and solving Bayesian decision problems and optimization problems. In this paper after introducing the valuation based system framework, we present Markov-like properties of VBS and a method for resolving queries to VBS. " } @article{andersen96linear, author = "K.A. Andersen and J.N. Hooker", title = "A linear programming framework for logics of uncertainty", journal = "Decision Support Systems", volume = "16", issue = "1", publisher = "Elsevier Science", pages = "39-53", year = "1996", abstract="Several logics for reasoning under uncertainty distribute ``probability mass'' over sets in some sense. These include probabilistic logic, Dempster-Shafer theory, other logics based on belief functions, and second-order probabilistic logic. We show that these logics are instances of a certain type of linear programming model, typically with exponentially many variables. We also show how a single linear programming package can implement these logics computationally if one ``plugs in'' a different column generation subroutine for each logic, although the practicality of this approach has been demonstrated so far only for probabilistic logic." } @article{ngwenyama98generating, author = "Ojelanki K. Ngwenyama and Noel Bryson", title = "Generating belief functions from qualitative preferences: An approach to eliciting expert judgments and deriving probability functions", journal = "Data and Knowledge Engineering", volume = "28", issue = "2", publisher = "Elsevier Science", pages = "145-159", year = "1998", abstract="It has long been recognized that the capability of using qualitative preferences to generate numeric judgments in expert systems and intelligent decision support systems (ES/IDSS) is essential. Although qualitative preferences and expressions facilitate communication and are useful for thinking about complex problems there is no simple and straightforward way to transform them for computer processing. Thus, the developer of the ES/IDSS must work with each expert to transform his/her vague and incomplete preferences into numeric estimates. This is a very difficult task and few techniques are available to assist developers with it. In this paper we present a qualitative discriminant process (QDP) for eliciting qualitative preferences from experts and generating appropriate numerical representations, as required by ES/IDSS, that utilize the Dempster-Shafer Theory. This approach provides a strategy for generating consistent numeric values for belief functions from qualitative preferences that can be used with the Dempster rules. We illustrate the approach with a case example." } @article{polkowski96mereology, author = "L. Polkowski and A. Skowron", title = "Rough Mereology: A New Paradigm for Approximate Reasoning", journal = "International Journal of Approximate Reasoning", volume = "15", issue = "4", publisher = "Elsevier Science", pages = "333-365", year = "1996", abstract="We are concerned with formal models of reasoning under uncertainty. Many approaches to this problem are known in the literature: Dempster-Shafer theory, bayesian-based reasoning, belief networks, fuzzy logics, etc. We propose rough mereology as a foundation for approximate reasoning about complex objects. Our notion of a complex object includes approximate proofs understood as schemes constructed to support our assertions about the world on the basis of our incomplete or uncertain knowledge." } @article{den99reasoning, author = "Thierry Denoeux", title = "Reasoning with imprecise belief structures", journal = "International Journal of Approximate Reasoning", volume = "20", issue = "1", publisher = "Elsevier Science", pages = "79-111", year = "1999", abstract="This paper extends the theory of belief functions by introducing new concepts and techniques, allowing to model the situation in which the beliefs held by a rational agent may only be expressed (or are only known) with some imprecision. Central to our approach is the concept of interval-valued belief structure (IBS), defined as a set of belief structures verifying certain constraints. Starting from this definition, many other concepts of Evidence Theory (including belief and plausibility functions, pignistic probabilities, combination rules and uncertainty measures) are generalized to cope with imprecision in the belief numbers attached to each hypothesis. An application of this new framework to the classification of patterns with partially known feature values is demonstrated." } @ARTICLE{bk95, AUTHOR = {P. Besnard and Jurg Kohlas}, TITLE = {Evidence Theory Based on General Consequence Relations}, JOURNAL = {Int. J. of Foundations of Computer Science}, YEAR = {1995}, VOLUME = {6}, NUMBER = {2}, PAGES = {119-135}, URL = {http://www2-iiuf.unifr.ch/tcs/publications/ps/bk95.ps.Z}, ABSTRACT = {The Dempster-Shafer theory of evidence can be conceived as a theory of probability of provability. In fact, it has been shown that evidence theory can be developed based on assumption based reasoning. Taking this approach, reasoning is modeled in this paper by a consequence relation in the sense of Tarski. It is shown that it is possible to construct evidence theory on top of the very general logics defined by these consequence relations. Support functions can be derived which are, as usual, set functions, monotone of infinite order. Furthermore, plausibility functions can also be defined. However, as negation is not generally defined in these general logics, the usual duality relations between support and plausibility functions of Dempster-Shafer theory do not hold in general. But this symmetry can be installed progressively by specializing to logics enjoying more and more ``structural properties''} } @article{yager99modeling, author = "Ronald R. Yager", title = "Modeling uncertainty using partial information", journal = "Information Sciences", volume = "121", issue = "3-4", publisher = "Elsevier Science", pages = "271-294", year = "1999", abstract="We are concerned here with the issue of representing the available information, which is often only partial, about the value of a variable. We consider the Dempster-Shafer belief structure and describe a number of different semantics that can be associated with it. Among these is a probabilistic interpretation in which some of the information is not available, we do not have all the distributions. This probabilistic interpretation leads us to consider a view involving selecting balls from an urn. Using this urn framework as a representation of our partial knowledge about the value of a variable leads to number of different uncertainty representations depending upon what information is assumed known." } @article{liu96theory, author = "Liping Liu", title = "A Theory of Gaussian Belief Functions", journal = "International Journal of Approximate Reasoning", volume = "14", issue = "2-3", publisher = "Elsevier Science", pages = "95-126", year = "1996", abstract="A Gaussian belief function can be intuitively described as a Gaussian distribution over a hyperplane, whose parallel subhyperplanes are the focal elements. This paper elaborates on the idea of Dempster and Shafer and formally represents a Gaussian belief function as a wide-sense inner product and a linear functional over a variable space, and as their duals over a hyperplane in a sample space. By adapting Dempster's rule to the continuous case, it derives a rule of combination and proves its equivalence to its geometric description by Dempster. It illustrates by examples how mixed knowledge involving linear equations, multivariate Gaussian distributions, and partial ignorance can be represented and combined as Gaussian belief functions." } @article{liu99local, author = "Liping Liu", title = "Local computation of Gaussian belief functions", journal = "International Journal of Approximate Reasoning", volume = "22", issue = "3", publisher = "Elsevier Science", pages = "217-248", year = "1999", abstract="Gaussian belief functions represent logical and probabilistic knowledge for mixed variables, some of which are deterministic, some vacuous, and some Gaussian. They include as special types linear equations, statistical observations, multivariate Gaussian distributions, and vacuous belief functions. The notion of Gaussian belief functions was proposed by A.P. Dempster (Normal belief functions and the Kalman filter, Technical report, Department of Statistics, Harvard University, Cambridge, MA, 1990.), formalized by G. Shafer (A note on Dempster's Gaussian belief functions, Technical report, School of Business, University of Kansas, Lawrence, KS, 1992.) and L. Liu (International Journal of Approximate Reasoning 14 (1996) 95-126.); (in: D. Fisher, Hans-J. Lenz (Eds.), Learning Models from Data: AI and Statistics V, Springer, New York, NY, 1996, pp. 79-88.) and successfully applied in combining independent statistical models in L. Liu (Model combination using Gaussian belief functions, Technical report, School of Business, University of Kansas, Lawrence, KS, 1995.). In this paper, we propose a join-tree computation scheme for expert systems using Gaussian belief functions. We first represent Dempster's rule of combination obtained in Liu (1996) alternatively in terms of matrix sweepings. We then show the operations of Gaussian belief functions follow the axioms of P.P. Shenoy and G. Shafer (in: R.D. Shachter, T.S. Levitt, L.N. Kanal, J.F. Lemmer (Eds.), Uncertainty in Artificial Intelligence, vol. 4, North-Holland, Amsterdam, 1990, pp. 169-198.) and justify the possibility of a join-tree computation scheme for Gaussian Belief functions. The result enriches the theory of local computation by extending its applicability to the combination of statistical models and the integration of knowledge bases. Examples are carried out to illustrate how combined inference can be made in accordance with multiple statistical models using graphically structured belief function models." } @article{snow98vulnerability, author = "Paul Snow", title = "The vulnerability of the transferable belief model to Dutch books", journal = "Artificial Intelligence", volume = "105", issue = "1-2", publisher = "Elsevier Science", pages = "345-354", year = "1998" } @article{smets94transferable, author = "Philippe Smets and Robert Kennes", title = "The transferable belief model ", journal = "Artificial Intelligence ", volume = "66", issue = "2", publisher = "Elsevier Science", pages = "191-234", year = "1994", abstract=" We describe the transferable belief model, a model for representing quantified beliefs based on belief functions. Beliefs can be held at two levels: (1) a credal level where beliefs are entertained and quantified by belief functions, (2) a pignistic level where beliefs can be used to make decisions and are quantified by probability functions. The relation between the belief function and the probability function when decisions must be made is derived and justified. Four paradigms are analyzed in order to compare Bayesian, upper and lower probability, and the transferable belief approaches." } @incollection{Lowrance90, author = "John D. Lowrance and T.D. Garvey and Thomas M. Strat", title = "A framework for evidential reasoning systems", booktitle= "Readings in uncertain reasoning", editor = "Shafer and Pearl", pages = "611-618", publisher= "Morgan Kaufman", year = "1990" } @incollection{Hsia89a, author = "Y. Hsia and Prakash P. Shenoy", title = "An evidential language for expert systems", booktitle= "Methodologies for Intelligent Systems", editor = "Ras Z.", pages = "9-16", publisher= "North Holland", year = "1989" } @incollection{Saffiotti91, author = "Alessandro Saffiotti", title = "A hybrid belief system for doubtful agents", booktitle= "Uncertatiny in Knowledge Bases, Lecture Notes in Computer Science 251", editor = "", pages = "393-402", publisher= "Springer-Verlag", year = "1991" } @incollection{smets91other, author = "Philippe Smets", title = "The transferable belief model and other interpretations of {D}empster-{S}hafer's model", booktitle= "Uncertainty in Artificial Intelligence, volume 6", editor = "P.P. Bonissone and M. Henrion and L.N. Kanal and J.F. Lemmer", pages = "375-383", publisher= "North-Holland, Amsterdam", year = "1991" } @incollection{Smets91a, author = "Philippe Smets and Y. T. Hsia and Alessandro Saffiotti and R. Kennes and H. Xu and E. Emkehrer", title = "The Transferable Belief Model", booktitle= "Symbolic and Quantitative Approaches to Uncertainty", editor = "Kruse R. and Siegel P.", pages = "91-96", publisher= "Springer Verlag, Lecture Notes in Computer Science No. 458, Berlin", year = "1991" } @inproceedings{Saffiotti90, author = "Alessandro Saffiotti", title = "A hybrid framework for representing uncertain knowledge", booktitle= "Procs. of the 8th AAAI Conf. Boston, MA", editor = "", journal= "", volume = "", pages = "653-658", year = "1990" } @inproceedings{smets00fusion, author = "Philippe Smets", title = "Data Fusion in the Transferable Belief Model", booktitle= "Proc. 3rd Intern. Conf. Inforation Fusion", editor = "", journal= "", volume = "", pages = "21-33", year = "Paris, France 2000" } @inproceedings{Lowrance86, author = "John D. Lowrance and T. D. Garvey and Thomas M. Strat", title = "A framework for evidential-reasoning systems", booktitle= "Proceedings of the National Conference on Artificial Intelligence", editor = "American Association for Artificial Intelligence", journal= "", volume = "", pages = "896-903", year = "1986" } @inproceedings{Zarley88a, author = "D.K. Zarley and Y.T. Hsia and Glenn Shafer", title = "Evidential reasoning using {DELIEF}", booktitle= "Proc. Seventh National Conference on Artificial Intelligence", editor = "", journal= "", volume = "1", pages = "205-209", year = "1988" } @inproceedings{Laskey88, author = "K. Laskey and P.E. Lehner", title = "Belief manteinance: an integrated approach to uncertainty management", booktitle= "Proceeding of the Seventh National Conference on Artificial Intelligence (AAAI-88)", editor = "", journal= "", volume = "1", pages = "210-214", year = "1988" } @techreport{Zarley88b, author = "D.K. Zarley", title = "An evidential reasoning system", institution = "No.206, University of Kansas", year = 1988, } @techreport{Lowrance87, author = "John D. Lowrance", title = "Evidential Reasoning with Gister: A Manual", institution = "Artificial Intelligence Center, SRI International, 333 Ravenswood Avenue, Menlo Park, CA.", year = 1987, } @techreport{Lowrance94, author = "John D. Lowrance", title = "Evidential Reasoning with Gister-CL: A Manual", institution = "Artificial Intelligence Center, SRI International, 333 Ravenswood Avenue, Menlo Park, CA.", year = 1994, } @techreport{Hsia89b, author = "Y. Hsia and Prakash P. Shenoy", title = "MacEvidence: A visual evidential language for knowledge-based systems", institution = "No 211, School of Business, University of Kansas", year = 1989, } %% continuous TOE @article{shafer79allocations, author = "Glenn Shafer", title = "Allocations of Probability", journal= "Annals of Probability", volume = "7:5", pages = "827-839", year = "1979" } %% computational analysis and algorithms @article{kennes92computational, author = "R. Kennes", title = "Computational Aspects of the Moebius Transformation of Graphs", journal= "IEEE Transactions on Systems, Man, and Cybernetics", volume = "22", pages = "201-223", year = "1992" } @article{tessem93approximations, author = "Bjornar Tessem", title = "Approximations for Efficient Computation in the Theory of Evidence", journal= "Artificial Intelligence", volume = "61:2", pages = "315-329", year = "1993" } @article{Shafer87a, author = "Glenn Shafer and R. Logan", title = "Implementing {D}empster's rule for hierarchical evidence", journal= "Artificial Intelligence", volume = "33", pages = "271-298", year = "1987", abstract="This article gives an algorithm for the exact implementation of Dempster's rule in the case of hierarchical evidence. This algorithm is computationally efficient, and it makes the approximation suggested by Gordon and Shortliffe unnecessary. The algorithm itself is simple, but its derivation depends on a detailed understanding of the interaction of hierarchical evidence." } @article{Shenoy86, author = "Glenn Shafer and Prakash P. Shenoy", title = "Propagating belief functions using local computations", journal= "IEEE Expert", volume = "1", pages = "(3), 43-52", year = "1986" } @ARTICLE{km91, AUTHOR = {Jurg Kohlas and Paul-Andr\'e Monney}, TITLE = {Propagating Belief Functions Through Constraint Systems}, JOURNAL = {Int. J. Approximate Reasoning}, YEAR = {1991}, VOLUME = {5}, PAGES = {433-461}, ABSTRACT = {} } @ARTICLE{xu96reasoning, AUTHOR = {H. Xu and Philippe Smets}, TITLE = {Reasoning in Evidential Networks with Conditional Belief Functions}, JOURNAL = {International Journal of Approximate Reasoning}, YEAR = {1996}, VOLUME = {14}, PAGES = {155-185}, ABSTRACT = {In the existing evidential networks applicable to belief functions, the relations among the variables are always represented by joint belief functions on the product space of the variables involved. In this paper, we use conditional belief functions to represent such relations in the network and show some relations between these two kinds of representations. We also present a propagation algorithm for such networks. By analyzing the properties of some special networks with conditional belief functions, called networks with partial dependency, we show that the computation for reasoning can be simplified.} } @article{xu95computing, author = "H. Xu", title = "Computing Marginals from the Marginal Representation in {M}arkov trees", journal= "Artificial Intelligence", volume = "74", pages = "177-189", year = "1995" } @ARTICLE{kohlas89b, AUTHOR = {Jurg Kohlas}, TITLE = {Modeling Uncertainty with Belief Functions in Numerical Models}, JOURNAL = {Europ. J. of Operational Research}, YEAR = {1989}, VOLUME = {40}, PAGES = {377--388}, ABSTRACT = {} } @incollection{Shenoy88, author = "Prakash P. Shenoy and K. Mellouli", title = "Propagation of belief functions: a distributed approach", booktitle= "Uncertainty in Artificial Intelligence 2", editor = "Lemmer and Kanal", pages = "325-336", publisher= " North Holland", year = "1988" } @incollection{Xu94, author = "H. Xu and R. Kennes", title = "Steps towards an Efficient Implementation of {D}empster-{S}hafer Theory", booktitle= "Advances in the Dempster-Shafer Theory of Evidence", editor = "R.R. Yager and M. Fedrizzi and J. Kacprzyk", pages = "153-174", publisher= "John Wiley and Sons, Inc.", year = "1994" } @incollection{Xu93, author = "H. Xu", title = "An Efficient Tool for Reasoning with Belief Functions Uncertainty in Intelligent Systems", booktitle= "Advances in the Dempster-Shafer Theory of Evidence", editor = "Bouchon-Meunier B., Valverde L. and Yager R. R.", pages = "215-224", publisher= "North-Holland: Elsevier Science", year = "1993" } @incollection{Thoma91, author = "H. M. Thoma", title = "Belief Function Computations", booktitle= "Conditional Logic in Expert Systems", editor = "", pages = "269-308", publisher= "North Holland", year = "1991" } @incollection{Wilson, author = "Nic Wilson", title = "Chapter 10 : Belief Functions Algorithms", booktitle= "Algorithms for Uncertainty and Defeasible Reasoning", editor = "", pages = "", publisher= "", year = "" } @inproceedings{Barnett81, author = "J.A. Barnett", title = "Computational methods for a mathematical theory of evidence", booktitle= "Proc. of the 7th National Conference on Artificial Intelligence (AAAI-88)", editor = "", journal= "", volume = "", pages = "868-875", year = "1981" } @inproceedings{Xu94a, author = "H. Xu", title = "Computing Marginals from the Marginal Representation in {M}arkov Trees", booktitle= "Proc. of the 5th International Conference on Information Proceeding and Management of Uncertainty in Knowledge-Based Systems", editor = "", journal= "", volume = "", pages = "275-280", year = "1994" } @inproceedings{Xu92, author = "H. Xu", title = "An Efficient Tool for Reasoning with Belief Functions", booktitle= "Proc. of the 4th International Conference on Information Proceeding and Management of Uncertainty in Knowledge-Based Systems", editor = "", journal= "", volume = "", pages = "65-68", year = "1992" } @inproceedings{Xu91, author = "H. Xu", title = "An Efficient Implementation of the Belief Function Propagation", booktitle= "Proc. of the 7th Uncertainty in Artificial Intelligence", editor = "D\'{A}mbrosio B. D., Smets Ph. and Bonissone P. P.", journal= "", volume = "", pages = "425-432", year = "1991" } @inproceedings{Lehmann99, author = "Norbert Lehmann and Rolf Haenni", title = "An alternative to outward propagation for {D}empster-{S}hafer Belief functions", booktitle= "Proceedings of The Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty - Ecsqaru ( Lecture Notes in Computer Science Series)", editor = "", journal= "", volume = "", pages = "", year = "London, 5-9 July 1999" } @INPROCEEDINGS{bissig97fastdivision, AUTHOR = {R. Bissig and Jurg Kohlas and N. Lehmann}, TITLE = {Fast-division architecture for {D}empster-{S}hafer belief functions}, BOOKTITLE = {Qualitative and Quantitative Practical Reasoning, First International Joint Conference on Qualitative and Quantitative Practical Reasoning; ECSQARU--FAPR'97 }, YEAR = {1997}, EDITOR = {D. Gabbay and R. Kruse and A. Nonnengart and H.J. Ohlbach}, PAGES = {}, PUBLISHER = {Springer}, BOOKTITEL = {Lecture Notes in Artif. Intell.}, NOTE = {}, URL = {http://www2-iiuf.unifr.ch/tcs/publications/ps/bkl97.ps.Z} } %% theoretical advances @PHDTHESIS{Kong86a, author = "Augustine Kong", title = "Multivariate belief functions and graphical models", school = "Harvard University", type = "{PhD} Dissertation", address = "Department of Statistics", month = "", year = 1986, note = "", } @PHDTHESIS{Mellouli86, author = "K. Mellouli", title = "On the propagation of beliefs in networks using the {D}empster-{S}hafer theory of evidence", school = "University of Kansas", type = "{PhD} Dissertation", address = "School of Business", month = "", year = 1986, note = "", } @article{krantz83priors, author = "David H. Krantz and John Miyamoto", title = "Priors and Likelihood Ratios as Evidence", journal = "Journal of the American Statistical Association", volume = " 78", issue = "382", publisher = "", pages = "418-423", year = "June 1983" } @article{yu94conditional, author = "Chunhai Yu and Fahard Arasta", title = "On Conditional Belief Functions", journal = "International Journal of Approxiomate Reasoning", volume = "10", issue = "", publisher = "Elsevier Science", pages = "155-172", year = "1994" } @article{Hajek96, author = "P. Hajek", title = "Getting Belief Functions from Kripke Models", journal = "International Journal of General Systems", volume = " 24", issue = "3", publisher = "", pages = "325-327", year = "1996" } @article{Kramosil95, author = "Ivan Kramosil", title = "Approximations of Believeability Functions under Incomplete Identification of Sets of Compatible States", journal = "Kybernetika", volume = "31", issue = "5", publisher = "", pages = "425-450", year = "1995" } @article{Kramosil96a, author = "Ivan Kramosil", title = "{D}empster-{S}hafer Theory with Indiscernible States and Observations", journal = "International Journal of General Systems", volume = "25", issue = "2", publisher = "", pages = "147-152", year = "1996" } @article{Kramosil88, author = "Ivan Kramosil", title = "Expert Systems with Non-Numerical Belief Functions", journal = "Problems of Control and Information Theory", volume = "17", issue = "5", publisher = "", pages = "285-295", year = "1988" } @article{bryson98qualitative, author = "Noel Bryson and Ayodele Mobolurin", title = "Qualitative discriminant approach for generating quantitative belief functions", journal = "IEEE Transactions on Knowledge and Data Engineering", volume = "10", issue = "2", publisher = "IEEE", pages = "345-348", year = "1998", abstract="We present an approach that will be useful in knowledge acquisition from experts on the degree of belief in, or the probability of, the truthfulness of various propositions. Its advantages include exploring the given problem situation using linguistic quantifiers; avoiding the premature use of numeric measures; and identifying input data that is inconsistent with the theory of belief functions. " } @article{chateauneuf00ambiguity, author = "A. Chateauneuf and J.-C. Vergnaud", title = "Ambiguity reduction through new statistical data", journal = "International Journal of Approximate Reasoning", volume = "24", issue = "2-3", publisher = "Elsevier Science", pages = "283-299", year = "2000", abstract="We provide some objective foundations for a belief revision process in a situation where (i) the decision-maker's initial probabilistic knowledge is imprecise and characterized by the core of a belief function, (ii) expected new data are themselves consistent with a belief function with known focal sets and (iii) the revision process is based on belief function combination. We study the properties of the information value for such a revising in the Gilboa-Schmeidler multi-prior model." } @article{Wasserman90prior, author = "L.A. Wasserman", title = "Prior envelopes based on belief functions", journal = "Annals of Statistics", volume = "18", issue = "1", publisher = "", pages = "454-464", year = "1990" } @article{dubois90, author = "D. Dubois and H. Prade", title = "Consonant approximations of belief functions", journal = "International Journal of Approximate Reasoning", volume = "4", issue = "", publisher = "", pages = "419-449", year = "1990" } @article{kramosil97belief, author = "Ivan Kramosil", title = "Belief functions generated by signed measures", journal = "Fuzzy Sets and Systems", volume = "92", issue = "2", publisher = "Elsevier Science", pages = "157-166", year = "1997", abstract="It is a well-known fact that the usual and already classical combinatorial definition of belief function over (the power-set of) a finite set can be generalized in such a way that belief function is defined by the quantile function of a set-valued (generalized) random variable defined over an abstract probability space. In this contribution we shall investigate a further stage of generalization resulting when the probability space in question is replaced by a measurable space equipped by a signed measure; signed measure is a «sigma»-additive set function which can take values also outside the unit interval, including the negative and infinite ones. An assertion analogous to the Jordan decomposition theorem for signed measures is stated and proved, according to which each signed belief function restricted to its finite values can be defined by a linear combination of two classical probabilistic belief functions, supposing that the basic set is finite." } @article{kramosil99measure-theoretic, author = "Ivan Kramosil", title = "Measure-theoretic approach to the inversion problem for belief functions", journal = "Fuzzy Sets and Systems", volume = "102", issue = "3", publisher = "Elsevier Science", pages = "363-369", year = "1999", abstract="The problem how to define an inverse operation to the Dempster combination rule for basic probability assignments and belief functions possesses a natural motivation and an intuitive interpretation. Or, if the Dempster rule reflects a modification of one's system of degrees of beliefs when the subject in question becomes familiar with the degrees of beliefs of another subject and accepts the arguments on which these degrees are based, the inverse operation would enable to erase the impact of this modification, and to return back to one's original degrees of beliefs, supposing that the reliability of the second subject is put into doubts. Within the algebraic framework this inversion problem was solved by Ph. Smets in [6], here we suggest an alternative solution based on the apparatus of measure theory and conserving the idea that degrees of beliefs are measures, i.e., numerically quantified sizes, of certain sets of elementary random events defined by set-valued random variables. However, probability measures, used for these purposes when defining classical belief functions, will be replaced by the so-called signed measures, which can also take values outside the unit interval of real numbers including the negative and even infinite ones." } @article{parsons96qualitative, author = "Simon Parsons and Alessandro Saffiotti", title = "A Case Study in the Qualitative Verification and Debugging of Numerical Uncertainty", journal = "International Journal of Approximate Reasoning", volume = "14", issue = "2-3", publisher = "Elsevier Science", pages = "187-216", year = "1996", abstract="Quantitative methods for reasoning under uncertainty have become well established, and many alternative formalisms have been suggested. In recent years there has been a growing interest in qualitative methods as helpful in situations in which the use of precise numerical methods is not appropriate. In this paper we demonstrate another use for qualitative models. The qualitative analysis of a quantitative model of uncertainty will reveal the qualitative behavior of that model when new evidence is obtained. This qualitative behavior may be studied to identify those situations in which the model does not behave as expected, and which quantitative values must be altered to correct this behavior. The demonstration is set within the context of the diagnosis of faults in an electricity network, and reports the results of the verification of a model representing a small fragment of a real application. The model was built using Pulcinella, a tool based on Shenoy and Shafer's valuation systems." } @article{resconi98speed-up, author = "G. Resconi and A.J. van der Wal and D. Ruan", title = "Speed-up of the Monte Carlo method by using a physical model of the {D}empster-{S}hafer theory", journal = "International Journal of Intelligent Systems", volume = "13", issue = "2", publisher = "John Wiley and Sons", pages = "221-242", year = "1998", abstract="A method that speed up the classical Monte Carlo method is presented. The method is based on the observation that the Boltzmann transition probability and the concept of local thermodynamical equilibrium give rise to an initial state of maximum entropy, which is subsequently modified by using the information on the internal structure of the system. To model the internal structure of the system, a physical model of the belief measure as defined in the Dempster-Shafer theory is proposed. An algorithm which calculate the probability distribution, gives way for utilizing the Boltzmann distribution to guide the Monte Carlo iterative method to obtain the global minimum value of the potential energy. " } @article{denneberg99interaction, author = "Dieter Denneberg and Michel Grabisch", title = "Interaction transform of set functions over a finite set", journal = "Information Sciences", volume = "121", issue = "1-2", publisher = "Elsevier Science", pages = "149-170", year = "1999", abstract="The paper introduces a new transform of set functions over a finite set, which is linear and invertible as the well-known Moebius transform in combinatorics. This transform leads to the interaction index, a central concept in multicriteria decision making. The interaction index of a singleton happens to be the Shapley value of the set function or, in terms of cooperative game theory, of the value function of the game. Properties of this new transform are studied in detail, and some illustrative examples are given." } @article{Shafer87b, author = "Glenn Shafer and Prakash P. Shenoy and K. Mellouli", title = "Propagating belief functions in qualitative {M}arkov trees", journal= "International Journal of Approximate Reasoning", volume = "1", pages = "(4), 349-400", year = "1987" } @article{murphy00combining, author = "Catherine K. Murphy", title = "Combining belief functions when evidence conflicts", journal = "Decision Support Systems", volume = "29", issue = "1", publisher = "Elsevier Science", pages = "1-9", year = "2000", abstract="The use of belief functions to represent and to manipulate uncertainty in expert systems has been advocated by some practitioners and researchers. Others have provided examples of counter-intuitive results produced by Dempster's rule for combining belief functions and have proposed several alternatives to this rule. This paper presents another problem, the failure to balance multiple evidence, then illustrates the proposed solutions and describes their limitations. Of the proposed methods, averaging best solves the normalization problems, but it does not offer convergence toward certainty, nor a probabilistic basis. To achieve convergence, this research suggests incorporating average belief into the combining rule." } @article{Fua86, author = "P. Fua", title = "Using Probability Density Functions in the Framework of Evidential Reasoning", journal= "Uncertainty in Knowledge-Based Systems, Lectures Notes in Computer science", volume = "286", pages = "243--252", year = "1986" } @article{Eddy86, author = "W.F. Eddy and G.P. Pei", title = "Structures of rule-based belief functions", journal= "IBM J.Res.Develop.", volume = "30", pages = "43-101", year = "1986" } @article{Jaffray92, author = "J. Y. Jaffray", title = "Bayesian updating and belief functions", journal= "IEEE Transactions on Systems, Man and Cybernetics", volume = "22", pages = "1144-1152", year = "1992" } @article{xu96some, author = "H. Xu and Philippe Smets", title = "Some Strategies for Explanations in Evidential Reasoning", journal= "IEEE Transactions on Systems, Man and Cybernetics", volume = "26:5", pages = "599-607", year = "1996" } @ARTICLE{kohlas93c, AUTHOR = "Jurg Kohlas", TITLE = "Support and Plausibility Functions Induced by Filter-Valued Mappings", JOURNAL = "Int. J. of General Systems", YEAR = "1993", VOLUME = "21", NUMBER = "4", PAGES = "343-363" } @ARTICLE{kohlas88b, AUTHOR = "Jurg Kohlas", TITLE = "Conditional Belief Structures", JOURNAL = "Probability in Engineering and Information Science", YEAR = "1988", VOLUME = "2", NUMBER = "4", PAGES = "415-433" } @article{websterii99vadidation, author = "Laurie Webster II and Jen-Gwo Chen and Simon S. Tan and Carolyn Watson and Andr\'e de Korvin", title = "Vadidation of authentic reasoning expert systems", journal = "Information Sciences", volume = "117", issue = "1-2", publisher = "Elsevier Science", pages = "19-46", year = "1999", abstract="This paper outlines an approach for validating the expert system's performance by comparing the expert system to the consensus results of the experts (i.e., using several experts to solve the same problem that the authentic reasoning expert system solved). We also discuss a mathematical process that includes the use of rough set theory as a means of capturing and quantifying the reasoning factors and reasoning processes of the experts. Additionally, a generalized entropy criterion for measuring consensus effectiveness based on Dempster-Shafer's theory of mathematical evidence is used in conjunction with rough set and fuzzy set theories. This is used for ascertaining whether or not the behavior of the expert system is evident in the behavior of the experts which is an essential task in validating authentic reasoning expert systems." } @article{maluf97monotonicity, author = "David A. Maluf", title = " Monotonicity of Entropy Computations in Belief Functions", journal = "Intelligent Data Analysis", volume = "1", issue = "3", publisher = "Elsevier Science", pages = "207-213", year = "1997", abstract="This article addresses the issue of quantitative information measurement within the Dempster-Shafer belief function formalism. Entropy computation in Dempster-Shafer depends on the way uncertainty measures are conceptualized. However, freed of most probability constraints, uncertainty measures in Dempster-Shafer theory can lead to further advances in optimization in information theory, which in turn may have a wide impact on decision and control. This article examines one form of current development regarding the entropy measure induced from the measure of dissonance. For a significant period, the measure of dissonance has been taken as a measure of entropy. We present in this article the entropy measure as a monotonically decreasing function, symmetrical to the measure of dissonance." } @INCOLLECTION{kb94, AUTHOR = {Jurg Kohlas and H.W. Brachinger}, TITLE = {Argumentation Systems and Evidence Theory}, BOOKTITLE = {Advances in Intelligent Computing -- IPMU'94, Paris}, ORGANIZATION = {Lecture Notes in Computer Science, no. 945 B}, PUBLISHER = {Springer}, YEAR = {1994}, EDITOR = {B. Bouchon-Meunier and R.R. Yager and L.A. Zadeh}, PAGES = {41--50} } @incollection{Augustin96, author = "T. Augustin", title = "Modeling weak information with generalized basic probability assignments", booktitle= "Data Analysis and Information Systems - Statistical and Conceptual Approaches", editor = "H. H. Bock and W. Polasek", pages = "101-113", publisher= "Springer", year = "1996" } @incollection{Saffiotti94a, author = "Alessandro Saffiotti", title = "Issues of knowledge representation in {D}empster-{S}hafer's theory", booktitle= "Advances in the Dempster-Shafer theory of evidence", editor = "R.R. Yager and M. Fedrizzi and J. Kacprzyk", pages = "415-440", publisher= "Wiley", year = "1994" } @inproceedings{smets95canonical, author = "Philippe Smets", title = "The Canonical Decomposition of a Weighted Belief", booktitle= "Proceedings of the International Joint Conference on AI, IJCAI’95", editor = "", journal= "", volume = "", pages = "1896-1901", year = "Montr\'eal, Canada, 1995" } @inproceedings{smets97FAPR1, author = "Philippe Smets", title = "The a-Junctions: the Commutative Combination Operators Applicable to Belief Functions", booktitle= "Proceedings of the International Joint Conference on Qualitative and Quantitative Practical Reasoning (ECSQARU / FAPR '97)", editor = "Gabbay D., Kruse R., Nonnengart A. and Ohlbach H. J. ", journal= "", volume = "", pages = "131-153", year = "Bad Honnef, Germany, 9-12 June 1997" } @inproceedings{kramosil93boolean, author = "Ivan Kramosil", title = "Toward a Boolean-Valued {D}empster-{S}hafer Theory", booktitle= "LOGICA '92", editor = "Svoboda V.", journal= "", volume = "", pages = "110-131", year = "Prague, 1993" } @inproceedings{kramosil94definability, author = "Ivan Kramosil", title = "Definability of Belief Functions over Countable Sets by Real-Valued Random Variables", booktitle= "IPMU. Information Processing and Management of Uncertainty in Knowledge-Based Systems", editor = "Svoboda V.", journal= "", volume = "3", pages = "49-50", year = "Paris, July 1994" } @inproceedings{kramosil94stronglaw, author = "Ivan Kramosil", title = "Strong Law of Large Numbers for Set-Valued Random Variables", booktitle= "Proceedings of the 3rd Workshop on Uncertainty Processing in Expert Systems", editor = "", journal= "", volume = "", pages = "122-142", year = "Prague, University of Economics, September 1994" } @inproceedings{kramosil96jordan, author = "Ivan Kramosil", title = "Jordan Decomposition of Signed Belief Functions", booktitle= "Proceedings of the international conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU'96)", editor = "", journal= "", volume = "", pages = "431-434", year = "Granada, Universidad de Granada, July 1996" } @inproceedings{Slobodová97, author = "Anna Slobodova", title = "Multivalued Extension of Conditional Belief Functions", booktitle= "Proceedings of the International Joint Conference on Qualitative and Quantitative Practical Reasoning (ECSQARU / FAPR '97)", editor = "", journal= "", volume = "", pages = "", year = "Bad Honnef, Germany, 9-12 June 1997" } @inproceedings{kramosil97measure, author = "Ivan Kramosil", title = "Measure-theoretic Approach to the Inversion Problem for Belief Functions", booktitle= "Proceedings of IFSA'97, Seventh International Fuzzy Systems Association World Congress", editor = "", journal= "", volume = "1", pages = "454-459", year = "Prague, Academia, June 1997" } @inproceedings{kramosil97nonstandard, author = "Ivan Kramosil", title = "Belief Functions with Nonstandard Values", booktitle= "Proceedings of Qualitative and Quantitative Practical Reasoning", editor = "Dav Gabbay and Rudolf Kruse and Andreas Nonnengart and H. J. Ohlbach", journal= "", volume = "", pages = "380-391", year = "Bonn, June 1997" } @inproceedings{Strat87, author = "Thomas M. Strat", title = "The generation of explanations within evidential reasoning systems", booktitle= "Proceedings of the Tenth Joint Conference on Artificial Intelligence", editor = "Institute of Electrical and Electronical Engineers", journal= "", volume = "", pages = "1097-1104", year = "1987" } @inproceedings{Strat84, author = "Thomas M. Strat", title = "Continuous belief functions for evidential reasoning", booktitle= "Proceedings of the National Conference on Artificial Intelligence", editor = "Institute of Electrical and Electronical Engineers", journal= "", volume = "", pages = "308-313", year = "August 1984" } @inproceedings{Xu95a, author = "H. Xu and Philippe Smets", title = "Generating Explanations for Evidential Reasoning", booktitle= "Proceedings of the 11th Uncertainty in Artificial Intelligence", editor = "Besnard Ph. and Hanks S. ", journal= "", volume = "", pages = "574-581", year = "1995" } @inproceedings{xu94evidential, author = "H. Xu and Philippe Smets", title = "Evidential Reasoning with Conditional Belief Functions", booktitle= "Proceedings of the 10th Uncertainty in Artificial Intelligence", editor = "Lopez de Mantaras R. and Poole D.", journal= "", volume = "", pages = "598-605", year = "1994" } @techreport{slobodova94conditional, author = "Anna Slobodova", title = "Conditional belief functions and valuation-based systems", institution = "Institute of Control Theory and Robotics, Slovak Academy of Sciences, Bratislava, SK", year = "1994", } @TECHREPORT{walley1982, author = {Peter Walley}, title = {The elicitation and aggregation of beliefs}, year = 1982, note = {Statistics Research Report 23}, address = {Coventry (U.K.)}, institution = {University of Warwick} } @TECHREPORT{kb95, AUTHOR = {Jurg Kohlas and P. Besnard}, TITLE = {An Algebraic Study of Argumentation Systems and Evidence Theory}, INSTITUTION = {Institute of Informatics, University of Fribourg}, YEAR = {1995}, NUMBER = {95--13}, URL = {http://www2-iiuf.unifr.ch/tcs/publications/ps/kb95.ps.Z}, ABSTRACT = {Argumentation systems permit to find arguments in favour and against hypotheses. And these hypotheses can be accepted as true or must be refuted as false according to whether the arguments supporting or refuting them are considered to be valid. Possibly the likelihood of arguments can be measured by probabilities. Then argumentation systems permit to define numerical degrees of support of hypotheses as the probability that arguments supporting the hypotheses are true. Similarly, numerical degrees of plausibility of hypotheses can be defined as the probability that arguments refuting the hypotheses do not hold. These probabilistic argumentation systems lead then to a Dempster-Shafer theory of evidence. In this paper first an algebraic theory of argumentation systems is developped based on general logical consequence relations and the notion of an allocation of support. In particular a computational theory for argumentation systems using local computations on hypertrees is studied on the fundaments of Shafer's paper ``An axiomatic study of computations in hypertrees''. This is then extended to probabilistic argumentation systems and evidence theory. The theory is last illustrated by an example, namely assumption-based reasoning.} } %% logic @article{provan90logicbased, author = "Gregory M. Provan", title = "A Logic-Based Analysis of {D}empster-{S}hafer Theory", journal = "International Journal of Approximate Reasoning", volume = "4", issue = "", publisher = "Elsevier Science Publishing Co., Inc.", pages = "451-495", year = "1990" } @article{harmanec94qualitative, author = "David Harmanec and Petr Hajek", title = "A qualitative belief logic", journal = "International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems", volume = "", issue = "", publisher = "", pages = "", year = "1994" } @article{tsiporkova99dempstershafer, author = "Elena Tsiporkova and Veselka Boeva and Bernard De Baets", title = "{D}empster-{S}hafer theory framed in modal logic", journal = "International Journal of Approximate Reasoning", volume = "21", issue = "2", publisher = "Elsevier Science", pages = "157-175", year = "1999", abstract="In this paper, the modal logic interpretation of plausibility and belief measures on an arbitrary universe of discourse, as proposed by Harmanec et al., is further developed by employing notions from set-valued analysis. In a model of modal logic, a multivalued mapping is constructed from the accessibility relation and a mapping determined by the value assignment function. This multivalued mapping induces a plausibility measure and a belief measure expressed in terms of conditional probabilities of inverse and superinverse images, or equivalently, in terms of conditional probabilities of truth sets of possibilitations and necessitations. Restricting to a finite universe of discourse, multivalued interpretations of basic probability assignments and of commonality functions are also obtained, in terms of conditional probabilities of pure inverse and subinverse images, or equivalently, in terms of conditional probabilities of truth sets of particular logical expressions involving possibilitations and necessitations." } @article{resconi96interpretations, author = "Germano Resconi and George J Klir and David Harmanec and Ute St Clair", title = "Interpretations of various uncertainty theories using models of modal logic: a summary", journal = "Fuzzy Sets and Systems", volume = "80", issue = "1", publisher = "Elsevier Science", pages = "7-14", year = "1996", abstract="This paper summarizes our efforts to establish the usual semantics of propositional modal logic as a unifying framework for various uncertainty theories. Interpretations for fuzzy set theory, Dempster-Shafer theory, probability theory, and possibility theory are discussed. Some properties of these interpretations are also presented, as well as directions for future research." } @inproceedings{Saffiotti92, author = "Alessandro Saffiotti", title = "A Belief Function Logic", booktitle= "Proceedings of the 10th AAAI Conf. San Jose, CA", editor = "", journal= "", volume = "", pages = "642-647", year = "1992" } @techreport{Walley82, author = "Peter Walley", title = "The elicitation and aggregation of beliefs", institution = "University of Warwick, Coventry (U.K.), Statistics Research Report 23", year = 1982, } %% reviews @ARTICLE{sheridan1991, author = {F. K. J. Sheridan}, title = {A survey of techniques for inference under uncertainty}, year = 1991, journal = {Artificial Intelligence Review}, volume = 5, pages = {89--119} } @article{cozman00reasoning, author = "Fabio G. Cozman and Seraf\'in Moral", title = "Reasoning with imprecise probabilities", journal = "International Journal of Approximate Reasoning", volume = "24", issue = "2-3", publisher = "Elsevier Science", pages = "121-123", year = "2000" } @article{klir95principles, author = "George J. Klir", title = "Principles of uncertainty: What are they? Why do we need them?", journal = "Fuzzy Sets and Systems", volume = "74", issue = "1", publisher = "Elsevier Science", pages = "15-31", year = "1995", abstract="The meaning and utility of three principles of uncertainty is discussed. These principles, which are referred to as a principle of minimum uncertainty, a principle of maximum uncertainty, and a principle of uncertainty invariance, depend on the theory in which uncertainty is conceptualized. Due to a connection between uncertainty and information, the principles may also be conceived as principles of information. To make the principles operational in a particular uncertainty theory, we need to measure the amount of relevant uncertainty (and associated information) in each problem situation describable within the theory. Well-justified measures of uncertainty have thus far been established only in some uncertainty theories. These theories, their uncertainty measures, and the associated uncertainty principles are overviewed in the paper." } @article{Kohlas94, author = "Jurg Kohlas and Paul-Andr\'e Monney", title = "Theory of Evidence - a Survey of its Mathematical Foundations, Applications and Computational Anaylsis", journal= "ZOR- Mathematical Methods of Operations Research", volume = "39", pages = "35--68", year = "1994" } @article{Saffiotti94b, author = "Alessandro Saffiotti and S. Parsons and E. Umkehrer", title = "Comparing uncertainty management techniques", journal= "Microcomputers in Civil Engineering", volume = "9", pages = "367-380", year = "1994" } @article{Dubois92, author = "Didier Dubois and Henri Prade", title = "Evidence, knowledge, and belief functions", journal= "International Journal of Approximate Reasoning", volume = "6", pages = "295-319", year = "1992" } @article{Fine77, author = "T. L. Fine", title = "Review of A Mathematical Theory of Evidence", journal= "Bulletin of the American Mathematical Society", volume = "83", pages = "667-672", year = "1977" } @article{Walley96, author = "Peter Walley", title = "Measures of uncertainty in expert systems", journal= "Artificial Intelligence", volume = "83", pages = "1-58", year = "1996", abstract="This paper compares four measures that have been advocated as models for uncertainty in expert systems. The measures are additive probabilities (used in the Bayesian theory), coherent lower (or upper) previsions, belief functions (used in the Dempster-Shafer theory) and possibility measures (fuzzy logic). Special emphasis is given to the theory of coherent lower previsions, in which upper and lower probabilities, expectations and conditional probabilities are constructed from initial assessments through a technique of natural extension. Mathematically, all the measures can be regarded as types of coherent lower or upper previsions, and this perspective gives some insight into the properties of belief functions and possibility measures. The measures are evaluated according to six criteria: clarity of interpretation; ability to model partial information and imprecise assessments, especially judgements expressed in natural language; rules for combining and updating uncertainty, and their justification; consistency of models and inferences; feasibility of assessment; and feasibility of computations. Each of the four measures seems to be useful in special kinds of problems, but only lower and upper previsions appear to be sufficiently general to model the most common types of uncertainty." } @article{dubois91epistemic, author = "Didier Dubois and Henri Prade", title = "Epistemic entrenchment and possibilistic logic", journal = "Artificial Intelligence", volume = "50", issue = "2", publisher = "Elsevier Science", pages = "223-239", year = "1991", abstract="This note points out the close relationships existing between recent proposals in the theory of belief revision made by Gardenfors based on the notion of epistemic entrenchment, and possibility theory applied to automated reasoning under uncertainty. It is claimed that the only numerical counterparts of epistemic entrenchment relations are so-called necessity measures that are dual to possibility measures, and are also mathematically equivalent to consonant belief functions in the sense of Shafer. Relationships between Spohn's ordinal conditional functions and possibility theory are also laid bare." } @article{roesmer00nonstandard, author = "Christopher Roesmer", title = "Nonstandard analysis and {D}empster-Shafer theory", journal = "International Journal of Intelligent Systems", volume = "15", issue = "2", publisher = "John Wiley and Sons", pages = "117-127", year = "2000", abstract="The Dempster-Shafer theory states that a number between zero and one is used to indicate one's degree of belief in a proposition A based on a body of difference. A different number between zero and one indicating one's degree of belief in proposition A may arise from a different body of evidence. Dempster-Shafer theory provides a way to combine these degrees of belief in proposition A. " } @INCOLLECTION{shafer1981b, author = {Glenn Shafer}, editor = {Asquith, P. and Hacking, I.}, title = {Two theories of probability}, year = 1981, volume = 2, booktitle = {Philosophy of Science Association Proceedings 1978}, publisher = {Philosophy of Science Association}, address = {East Lansing (MI)} } @INCOLLECTION{walley1997c, author = {Peter Walley}, editor = {Read, C. B. and Banks, D. L. and Kotz, S.}, title = {Imprecise probabilities}, year = 1997, booktitle = {The Encyclopedia of Statistical Sciences}, publisher = {Wiley}, address = {New York (NY)} } @INCOLLECTION{kohlas95b, AUTHOR = {Jurg Kohlas}, TITLE = {The Mathematical Theory of Evidence -- A Short Introduction}, BOOKTITLE = {System Modelling and Optimization}, PUBLISHER = {Chapman and Hall}, YEAR = {1995}, EDITOR = {J. Dolezal}, PAGES = {37--53}, ABSTRACT = {} } @incollection{dubois90modeling, author = "Didier Dubois and Henri Prade", title = "Modeling uncertain and vague knowledge in possibility and evidence theories", booktitle= "Uncertainty in Artificial Intelligence, volume 4", editor = "R. D. Shachter and T. S. Levitt and L. N. Kanal and J. F. Lemmer", pages = "303-318", publisher= "North-Holland", year = "1990" } @techreport{Kong86b, author = "A.P. Dempster and Augustine Kong", title = "Uncertain evidence and artificial analysis", institution = "S-108, Department of Statistics, Harvard University", year = 1986, } @TECHREPORT{kohlas87b, AUTHOR = {Jurg Kohlas}, TITLE = {The Logic of Uncertainty. Potential and Limits of Probability. Theory for Managing Uncertainty in Expert Systems}, INSTITUTION = {Institute for Automation and Operations Research, University of Fribourg}, YEAR = {1987}, NUMBER = {142} } @TECHREPORT{kohlas86, AUTHOR = {Jurg Kohlas}, TITLE = {Modeling Uncertainty for Plausible Reasoning with Belief}, INSTITUTION = {Institute for Automation and Operations Research, University of Fribourg}, YEAR = {1986}, NUMBER = {116} } %% Dempster's rule @article{shafer82bayes, author = "Glenn Shafer", title = "Bayes's Two Arguments for the Rule of Conditioning", journal= "Annals of Statistics", volume = "10:4", pages = "1075-1089", year = "December 1982" } @article{dasilva92algorithms, author = "Wagner Texeira da Silva and Ruy Luiz Milidiu", title = "Algorithms for Combining Belief Functions", journal= "International Journal of Approximate Reasoning", volume = "7", pages = "73-94", year = "1992" } @article{sudkamp92consistency, author = "Thomas Sudkamp", title = "The Consistency of {D}empster-{S}hafer Updating", journal= "International Journal of Approximate Reasoning", volume = "7", pages = "19-44", year = "1992" } @article{durham92statistical, author = "Stephen D. Durham and Jeffery S. Smolka and Marco Valtorta", title = "Statistical Consistency with {D}empster's Rule on Diagnostic Trees Having Uncertain Performance Parameters", journal= "International Journal of Approximate Reasoning", volume = "6", pages = "67-81", year = "1992" } @article{dempster67multivariate, author = "A.P. Dempster", title = "Upper and lower probabilities induced by a multivariate mapping", journal= "Annals of Mathematical Statistics", volume = "38", pages = "325-339", year = "1967" } @article{Dempster68a, author = "A.P. Dempster", title = "Upper and lower probabilities generated by a random closed interval", journal= "Annals of Mathematical Statistics", volume = "39", pages = "957-966", year = "1968" } @article{Dempster68b, author = "A.P. Dempster", title = "A generalization of {B}ayesian inference", journal= "Journal of the Royal Statistical Society, Series B", volume = "30", pages = "205-247", year = "1968" } @article{Dempster69, author = "A.P. Dempster", title = "Upper and lower probabilities inferences for families of hypothesis with monotone density ratios", journal= "Annals of Mathematical Statistics", volume = "40", pages = "953-969", year = "1969" } @article{Shafer86, author = "Glenn Shafer", title = "The combination of evidence", journal= "International Journal of Intelligent Systems", volume = "1", pages = "155-179", year = "1986" } @article{Zadeh86, author = "Lofti A. Zadeh", title = "A simple view of the {D}empster-{S}hafer theory of evidence and its implications for the rule of combination", journal= "AI Magazine", volume = "7:2", pages = "85-90", year = "1986" } @article{Voorbraak91, author = "F. Voorbraak", title = "On the justification of {D}empster's rule of combination", journal= "Artificial Intelligence", volume = "48", pages = "171-197", year = "1991" } @article{voorbraak89efficient, author = "F. Voorbraak", title = "A computationally efficient approximation of {D}empster-{S}hafer theory", journal= "International Journal on Man-Machine Studies", volume = "30", pages = "525-536", year = "1989" } @article{Wilson92, author = "Nic Wilson", title = "The combination of belief: when and how fast?", journal= "International Journal of Approximate Reasoning", volume = "6", pages = "377-388", year = "1992" } @article{orponen90dempster, author = "Pekka Orponen", title = "{D}empster's rule of combination is NP-complete", journal = "Artificial Intelligence", volume = "44", issue = "1-2", publisher = "Elsevier Science", pages = "245-253", year = "1990", abstract="We consider the complexity of combining bodies of evidence according to the rules of the Dempster-Shafer theory of evidence. We prove that, given as input a set of tables representing basic probability assignments m1, ..., mn, over a frame of discernment , and a set A , the problem of computing the combined basic probability value (m1 ··· mn)(A) is NP-complete. As a corollary, we obtain that while the simple belief, plausibility, and commonality values Bel(A), Pl(A), and Q(A) can be computed in polynomial time, the problems of computing the combinations (Bel1 ··· Beln)(A), (Pl1 ··· Pln)(A), and (Q1 ··· Qn)(A) are NP-complete." } @incollection{fagin91new, author = "R. Fagin and Joseph Y. Halpern", title = "A New Approach to Updating Beliefs", booktitle= "Uncertainty in Artificial Intelligence, 6", editor = "P.P. Bonissone, M. Henrion, L.N. Kanal and J.F. Lemmer", pages = "347-374", publisher= "", year = "1991" } @inproceedings{Ginsberg84, author = "M. L. Ginsberg", title = "Non-monotonic reasoning using {D}empster's rule", booktitle= "Proc. 3rd National Conference on AI (AAAI-84)", editor = "", journal= "", volume = "", pages = "126-129", year = "1984" } @inproceedings{kramosil97dempster, author = "Ivan Kramosil", title = "A Probabilistic Analysis of {D}empster Combination Rule", booktitle= "The Logica. Yearbook 1997", editor = " Childers Timothy", journal= "", volume = "", pages = "174-187", year = "Prague, 1997" } @inproceedings{Moral99, author = "Serafin Moral and Antonio Salmeron", title = "A {M}onte-{C}arlo algorithm for combining {D}empster-{S}hafer belief based on approximate pre-computation", booktitle= "Proceedings of The Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty - Ecsqaru ( Lecture Notes in Computer Science Series)", editor = "", journal= "", volume = "", pages = "", year = "London, 5-9 July 1999" } %% statistical inference and parametric estimation @article{Shafer82, author = "Glenn Shafer", title = "Belief functions and parametric models", journal= "Journal of the Royal Statistical Society", volume = "B.44", pages = "322-352", year = "1982" } @article{Walley87, author = "Peter Walley", title = "Belief function representations of statistical evidence", journal= "The Annals of Statistics", volume = "15", pages = "1439-1465", year = "1987" } @article{Wasserman90, author = "L. A. Wasserman", title = "Belief functions and statistical inference", journal= "Canadian Journal of Statistics", volume = "18", pages = "183-196", year = "1990" } @article{Beran71, author = "R. J. Beran", title = "On distribution-free statistical inference with upper and lower probabilities", journal= "Annals of Mathematical Statistics", volume = "42", pages = "157-168", year = "1971" } @article{Chen95, author = "Y. Y. Chen", title = "Statistical inference based on the possibility and belief measures", journal= "Transactions of the American Mathematical Society", volume = "347", pages = "1855-1863", year = "1995" } @TECHREPORT{kohlas92, AUTHOR = {Jurg Kohlas}, TITLE = {Evidential Reasoning About Parametric Models}, INSTITUTION = {Institute for Automation and Operations Research, University Fribourg}, YEAR = {1992}, TYPE = {}, NUMBER = {194}, ABSTRACT = {} } %% applications @article{iancu97prosum, author = "I. Iancu", title = "Prosum-prolog system for uncertainty management", journal = "International Journal of Intelligent Systems", volume = "12", issue = "9", publisher = "John Wiley and Sons", pages = "615-627", year = "1997", abstract="In this paper we present a system which uses knowledge represented in the form of production rules accompanied by uncertainty degrees. The uncertainty of a rule is given by using the method from SLOP and FRIL: a support pair, which comprises a necessary and possible support and can be interpreted as an interval in which the unknown probability lies. Giving the knowledge in this form, our system generates a Turbo Prolog program which has included the operations for uncertainty management. In this version, two kinds of rules for support logic programming are implemented but the user can propose the other ones, by using the dialogue with the system. Semantic unification differs from that used in FRIL; we use generalized belief functions. " } @article{giacinto97application, author = "G. Giacinto and R. Paolucci and F. Roli", title = "Application of neural networks and statistical pattern recognition algorithms to earthquake risk evaluation", journal = "Pattern Recognition Letters", volume = "18", issue = "11-13", publisher = "Elsevier Science", pages = "1353-1362", year = "1997" } @article{mcclean97evidence, author = "Sally McClean and Bryan Scotney", title = "Using evidence theory for the integration of distributed databases", journal = "International Journal of Intelligent Systems", volume = "12", issue = "10", publisher = "John Wiley and Sons", pages = "763-776", year = "1997", abstract="Distributed databases allow us to integrate data from different sources which have not previously been combined. In this article, we are concerned with the situation where the data sources are held in a distributed database. Integration of the data is then accomplished using the Dempster-Shafer representation of evidence. The weighted sum operator is developed and this operator is shown to provide an appropriate mechanism for the integration of such data. This representation is particularly suited to statistical samples which may include missing values and be held at different levels of aggregation. Missing values are incorporated into the representation to provide lower and upper probabilities for propositions of interest. The weighted sum operator facilitates combination of samples with different classification schemes. Such a capability is particularly useful for knowledge discovery when we are searching for rules within the concept hierarchy, defined in terms of probabilities or associations. By integrating information from different sources, we may thus be able to induce new rules or strengthen rules which have already been obtained. We develop a framework for describing such rules and show how we may then integrate rules at a high level without having to resort to the raw data, a useful facility for knowledge discovery where efficiency is of the essence. " } @article{buede97target, author = "Dennis M. Buede and Paul Girardi", title = "Target identification comparison of {B}ayesian and {D}empster-{S}hafer multisensor fusion", journal = "IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans.", volume = "27", issue = "5", publisher = "IEEE", pages = "569-577", year = "1997", abstract = "This paper demonstrates how Bayesian and evidential reasoning can address the same target identification problem involving multiple levels of abstraction, such as identification based on type, class, and nature. In the process of demonstrating target identification with these two reasoning methods, we compare their convergence tune to a long run asymptote for a broad range of aircraft identification scenarios that include missing reports and misassociated reports. Our results show that probability theory can accommodate all of these issues that are present in dealing with uncertainty and that the probabilistic results converge to a solution much faster than those of evidence theory. " } @article{liu97method, author = "Jiming Liu and Michel C. Desmarais", title = "Method of learning implication networks from empirical data: algorithm and Monte-Carlo simulation-based validation", journal = "IEEE Transactions on Knowledge and Data Engineering", volume = "9", issue = "6", publisher = "IEEE", pages = "990-1004", year = "1997", abstract="An algorithmic means for inducing implication networks from empirical data samples are described. The induced network enables efficient inferences about the values of network nodes if certain observations are made. This implication induction method is approximate in nature as probabilistic network requirements are relaxed in the construction of dependence relationships based on statistical testing. The effectiveness and validity of the induction method are examined by conducting Monte Carlo simulations. The values in the implication networks are also predicted by applying a modified version of the Dempster-shafer belief updating scheme. " } @article{fortemps97jobshop, author = "Philippe Fortemps", title = "Jobshop scheduling with imprecise durations: A fuzzy approach", journal = "IEEE Transactions on Fuzzy Systems", volume = "5", issue = "4", publisher = "IEEE", pages = "557-569", year = "1997", abstract="Jobshop scheduling problems are NP-hard problems. The durations in the reality of manufacturing are often imprecise and the imprecision in data is very critical for the scheduling procedures. Therefore, the fuzzy approach, in the framework of the Dempster-Shafer theory, commands attention. The fuzzy numbers are considered as sets of possible probabilistic distributions. After a review of some issues concerning fuzzy numbers, we discuss the determination of a unique optimal solution of the problem and then we cast a meta-heuristic (simulated annealing - SA) to this particular framework for optimization. It should be stressed that the obtained schedule remains feasible for all realizations of the operations durations. " } @article{xia97driven, author = "Yan Xia and S.S. Iyengar and N.E. Brener", title = "An event driven integration reasoning scheme for handling dynamic threats in an unstructured environment", journal = "Artificial Intelligence", volume = "95", issue = "1", publisher = "Elsevier Science", pages = "169-186", year = "1997", abstract="This paper presents an attempt to devise and develop a domain-independent reasoning system (DIRS) scheme for handling dynamic threats, and uses the scheme for automated route planning of military vehicles in an unstructured environment. Automated route planning is a very important branch in applications of artificial intelligence. In a dynamic unstructured environment, instead of simply using static cost from a mobility model, a dynamic cost surface is constructed in which the total cost is a linear combination of the static cost and the dynamic cost. The principal contributions of this paper are as follows: (i) A reasoning model called DIRS is proposed to quantitatively embed dynamic information, coordinate use of static and dynamic information, and handle real time events that happen outside the system. (ii) A temporal relation is applied in the route planning process for handling dynamic threats. (iii) Dempster-Shafer evidential theory is used to evaluate propagation of a dynamic threat. (iv) A detailed experimental analysis on automated route planning of military vehicles was conducted to study the performance of the DIRS model." } @article{gillett00monetary, author = "Peter R. Gillett", title = "Monetary unit sampling: a belief-function implementation for audit and accounting applications", journal = "International Journal of Approximate Reasoning", volume = "25", issue = "1", publisher = "Elsevier Science", pages = "43-70", year = "2000", abstract="Audit procedures may be planned and audit evidence evaluated using monetary unit sampling (MUS) techniques within the context of the Dempster-Shafer theory of belief functions. This article shows: (1) how to determine an appropriate sample size for MUS in order to obtain a desired degree of belief that the upper bound for misstatements lies within a given interval; and (2) what level of belief in a specified interval is obtained given a sample result. The results are consistent with the view that a specified level of belief in an interval is semantically a stronger claim than the same numerical level of probability. The paper describes two variants of MUS in both probability and belief-function forms, emphasizing the systematic similarities and the numerical differences between the two frameworks. The results, based on the Poisson distribution, extend results already available for mean-per-unit variables sampling, and may readily be developed to give similar results for the binomial distribution." } @article{golshani96dynamic, author = "Forouzan Golshani and Enrique Cortes-Rello and Thomas H. Howell", title = "Dynamic route planning with uncertain information", journal = "Knowledge-based Systems", volume = "9", issue = "4", publisher = "Elsevier Science", pages = "223-232", year = "1996", abstract="Navigating an autonomous vehicle through a threatening zone whose characteristics may change in an unpredictable manner is an important problem that has received much attention in the recent past. The paper describes the design of a route planning system, called RUTA-100, that works with incomplete information obtained from many unreliable knowledge sources and plans an optimal route by minimizing both danger and distance. The operation of the route planner has two main phases: the initial route planning phase and the dynamic plan execution. Once a point of origin and a point of destination have been identified, the route planner determines the optimal route based on the information available at that time. Should conditions change during plan execution, the route is accordingly recalculated. This is repeated until the destination point is reached. The Dempster-Shafer theory of belief is used as the underlying formalism to pool and represent uncertain information and reason with it." } @article{utete99voting, author = "Simukai W. Utete and Billur Barshan and Birsel Ayrulu", title = "Voting as validation in robot programming", journal = "International Journal of Robotics Research", volume = "18", issue = "4", publisher = "Sage Science Press", pages = "401-413", year = "1999", abstract="This paper investigates the use of voting as a conflict-resolution technique for data analysis in robot programming. Voting represents an information-abstraction technique. It is argued that in some cases a voting approach is inherent in the nature of the data being analyzed: where multiple, independent sources of information must be reconciled to give a group decision that reflects a single outcome rather than a consensus average. This study considers an example of target classification using sonar sensors. Physical models of reflections from target primitives that are typical of the indoor environment of a mobile robot are used. Dispersed sensors take decisions on target type, which must then be fused to give the single group classification of the presence or absence and type of a target. Dempster-Shafer evidential reasoning is used to assign a level of belief to each sensor decision. The decisions are then fused by two means. Using Dempster's rule of combination, conflicts are resolved through a group measure expressing dissonance in the sensor views. This evidential approach is contrasted with the resolution of sensor conflict through voting. It is demonstrated that abstraction of the level of belief through voting proves useful in resolving the straightforward conflicts that arise in the classification problem. Conflicts arise where the discriminant data value, an echo amplitude, is most sensitive to noise. Fusion helps to overcome this vulnerability: in Dempster-Shafer reasoning, through the modeling of nonparametric uncertainty and combination of belief values; and in voting, by emphasizing the majority view. The paper gives theoretical and experimental evidence for the use of voting for data abstraction and conflict resolution in areas such as classification, where a strong argument can be made for techniques that emphasize a single outcome rather than an estimated value. Methods for making the vote more strategic are also investigated. The paper addresses the reduction of dimension of sets of decision points or decision makers. Through a consideration of combination/order, queuing criteria for more strategic fusion are identified. " } @article{bell96generalized, author = "D.A. Bell and J.W. Guan and Suk Kyoon Lee", title = " Generalized union and project operations for pooling uncertain and imprecise information ", journal = "Data and Knowledge Engineering", volume = "18", issue = "2", publisher = "Elsevier Science", pages = "89-117", year = "1996" } @article{gordon85method, author = "Jean Gordon and Edward H. Shortliffe", title = "A method for managing evidential reasoning in a hierarchical hypothesis space", journal = "Artificial Intelligence", volume = "26", issue = "3", publisher = "Elsevier Science", pages = "323-357", year = "1985" } @article{dubitzky99towards, author = "Werner Dubitzky and Alex G. Büchner and John G. Hughes and David A. Bell", title = "Towards concept-oriented databases", journal = "Data and Knowledge Engineering", volume = "30", issue = "1", publisher = "Elsevier Science", pages = "23-55", year = "1999" } @article{Pagac98, author = "Daniel Pagac and Eduardo M. Nebot and Hugh Durrant-Whyte", title = "An Evidential Approach to Map-Bulding for Autonomous Vehicles", journal= "IEEE Transactions on Robotics and Automation", volume = "14, No 4", pages = "623-629", year = "August 1998", abstract="In this work, we examine the problem of constructing and maintaining a map of an autonomous vehicle's environment for the purpose of navigation, using evidential reasoning. The inherent uncertainty in the origin of measurements of sensors demands a probabilistic approach to processing, or fusing, the new sensory information to build an accurate map. In this paper, the map is based on a two-dimensional (2-D) occupancy grid. The sensor readings are 'fused' into the map using the Dempster-Shafer inference rule. This evidential approach with its multivalued hypotheses allows quantitative analysis of the quality of the data. The map building system is experimentally evaluated using sonar data from real environments. " } @article{hodges99development, author = "J. Hodges and S. Bridges and C. Sparrow and B. Wooley and B. Tang and C. Jun", title = "The development of an expert system for the characterization of containers of contaminated waste", journal = "Expert Systems with Applications", volume = "17", issue = "3", publisher = "Elsevier Science", pages = "167-181", year = "1999", abstract="Scientists at the Mississippi State University Diagnostic Instrumentation and Analysis Laboratory and the Idaho National Engineering and Environmental Laboratory are developing an expert system to aid in the determination of the proper disposition of containers of transuranic and low-level-alpha-contaminated waste generated as a byproduct of Department of Energy defense-related programs. This system will consider a variety of information such as real-time radiography and the data from both passive and active neutron assay systems to classify the containers into one of the two categoriesthose that meet the requirements for being shipped to the Waste Isolation Pilot Plant in New Mexico and those that do not. We describe the development of a prototype of the expert system. We also describe the approach used to represent and reason with information from a variety of sources as well as the uncertainty that is inherent in such information. We discuss the strengths and weaknesses of the various artificial intelligence techniques that were considered for use in the expert system." } @article{Srivastava89, author = "Glenn Shafer and R. Srivastava", title = "The {B}ayesian and belief-function formalism: A general perspective for auditing", journal= "Auditing: A Journal of Practice and Theory", volume = "", pages = "", year = "1989" } @article{Stokke94a, author = "P. R. Stokke and T. A. Boyce and John D. Lowrance and J. William and K. Ralston", title = "Industrial project monitoring with evidential reasoning", journal= "Nordic Advanced Information Technology Magazine", volume = "8", pages = "18--27", year = "1994" } @article{Stokke94b, author = "P. R. Stokke and T. A. Boyce and John D. Lowrance and J. William and K. Ralston", title = "Evidential reasoning and project early warning systems", journal= "Research and Technology Management", volume = "", pages = "", year = "1994" } @article{smets78theory, author = "Philippe Smets", title = "Theory of Evidence and Medical Diagnostic", journal= "Medical Informatics Europe", volume = "78", pages = "285-291", year = "1978" } @article{rakar99transferable, author = "Andrej Rakar and Ani Jurii and Peter Ball\'e", title = "Transferable belief model in fault diagnosis", journal = "Engineering Applications of Artificial Intelligence", volume = "12", issue = "5", publisher = "Elsevier Science", pages = "555-567", year = "1999", abstract="The Transferable Belief Model (TBM) is an approximate reasoning approach which is derived from the Dempster-Shafer mathematical theory of evidence. The key property of TBM is its ability to treat inconsistency in data by a novel concept of assigning belief, referred to as the `open-world' assumption. The aim of this paper is to apply TBM to a diagnostic framework, and to provide a detailed study of its most important features. The TBM approach is compared with fuzzy logic and conventional Boolean technique. It is further shown that the `open-world' assumption can be easily incorporated into the fuzzy logic context, resulting in comparable diagnostic outputs, even in cases of measurement noise and modelling errors. In addition, these novel reasoning approaches provide a measure of confidence in the underlying diagnostic results, which contributes a new quality to the diagnostic practice. Finally, the underlying methods are applied to a DC motor test rig. Practical results clearly show how TBM, along with its fuzzy counterpart, outperforms Boolean reasoning." } @article{Gordon85, author = "J. Gordon and Edward H. Shortliffe", title = "A method for managing evidential reasoning in hierarchical hypothesis spaces", journal= "Artificial Intelligence", volume = "26", pages = "323-358", year = "1985" } @article{murphy98dempster, author = "Robin R. Murphy", title = "Dempster-{S}hafer theory for sensor fusion in autonomous mobile robots", journal = "IEEE Transactions on Robotics and Automation", volume = "14", issue = "2", publisher = "IEEE", pages = "197-206", year = "1998", abstract="This article discusses Dempster-Shafer (DS) theory in terms of its utility for sensor fusion for autonomous mobile robots. It exploits two little used components of DS theory: the weight of conflict metric and the enlargement of the frame of discernment. The weight of conflict is used to measure the amount of consensus between different sensors. A lack of consensus leads the robot to either compensate within certain limits or investigate the problem further, adding robustness to the robot's operation. Enlarging the frame of discernment allows a modular decomposition of evidence. This decomposition offers the advantages of perceptual abstraction, and permits expert knowledge about the domain to be embedded in the frames of discernment, simplifying the construction and maintenance of the knowledge base. Six experiments using this Dempster-Shafer framework are presented. Data from four types of sensor data were collected by a mobile robot and fused with the Sensor Fusion Effects (SFX) architecture. " } @article{mcclean00background, author = "Sally McClean and Bryan Scotney and Mary Shapcott", title = "Using background knowledge in the aggregation of imprecise evidence in databases", journal = "Data and Knowledge Engineering", volume = "32", issue = "2", publisher = "Elsevier Science", pages = "131-143", year = "2000", abstract="Background knowledge of data is often available, arising from a concept hierarchy, as integrity constraints, from database integration, or from knowledge possessed by domain experts. Frequently databases contain incomplete data which we may represent using Dempster-Shafer mass functions to represent evidence contained in subsets of the domain. These subsets may be represented in the database as partial values which are derived from background knowledge using logic programming to re-engineer the database. For such a data model we develop an aggregation operator which calculates Dempster-Shafer mass functions and thus facilities decision making and knowledge discovery in databases." } @incollection{Biswas89, author = "G. Biswas and T. S. Anand", title = "Using the {D}empster-{S}hafer scheme in a mixed-initiative expert system shell", booktitle= "Uncertainty in Artificial Intelligence, volume 3", editor = "L.N. Kanal and T.S. Levitt and J.F. Lemmer", pages = "223-239", publisher= "North-Holland", year = "1989" } @inproceedings{Palacharla94b, author = "P. Palacharla and P.C. Nelson", title = "Evidential Reasoning in Uncertainty for Data Fusion", booktitle= "Proceedings of the Fifth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems", editor = "", journal= "", volume = "1", pages = "715-720", year = "1994" } %% decision and classification @ARTICLE{einhorn1986, author = {H. J. Einhorn and R. M. Hogarth}, title = {Decision making under ambiguity}, year = 1986, journal = {Journal of Business}, volume = 59, pages = {S225--S250} } @article{zouhal98evidence, author = "Lalla Meriem Zouhal and Thierry Denoeux", title = "Evidence-theoretic k-NN rule with parameter optimization", journal = "IEEE Transactions on Systems, Man and Cybernetics Part C: Applications and Reviews", volume = "28", issue = "2", publisher = "IEEE", pages = "263-271", year = "1998", abstract="This paper presents a learning procedure for optimizing the parameters in the evidence-theoretic k-nearest neighbor rule, a pattern classification method based on the Dempster-Shafer theory of belief functions. In this approach, each neighbor of a pattern to be classified is considered as an item of evidence supporting certain hypotheses concerning the class membership of that pattern. Based on this evidence, basic belief masses are assigned to each subset of the set of classes. Such masses are obtained for each of the k-nearest neighbors of the pattern under consideration and aggregated using the Dempster's rule of combination. In many situations, this method was found experimentally to yield lower error rates than other methods using the same information. However, the problem of tuning the parameters of the classification rule was so far unresolved. In this paper, we determine optimal or near-optimal parameter values from the data by minimizing an error function. This refinement of the original method is shown experimentally to result in substantial improvement of classification accuracy. " } @article{Caselton92, author = "W. F. Caselton and W. Luo", title = "Decision making with imprecise probabilities: {D}empster-{S}hafer theory and application", journal= "Water Resources Research", volume = "28", pages = "3071-3083", year = "1992" } @article{Jaffray94, author = "J. Y. Jaffray and P. P. Wakker", title = "Decision making with belief functions: compatibility and incompatibility with the sure-thing principle", journal= "Journal of Risk and Uncertainty", volume = "8", pages = "255-271", year = "1994" } @article{Strat90, author = "Thomas M. Strat", title = "Decision analysis using belief functions", journal= "International Journal of Approximate Reasoning", volume = "4", pages = "391-417", year = "1990" } @article{strat89explaining, author = "Thomas M. Strat and John D. Lowrance", title = "Explaining Evidential Analysis", journal= "International Journal of Approximate Reasoning", volume = "3", pages = "299-353", year = "1989" } @article{xu96transferable, author = "Hong Xu and Y.T. Hsia and Philippe Smets", title = "Transferable Belief Model for Decision Making in Valuation Based Systems", journal= "IEEE Transactions on Systems, Man, and Cybernetics", volume = "26:6", pages = "698-707", year = "1996" } @article{xu97valuation, author = "Hong Xu", title = "Valuation-based systems for decision analysis using belief functions", journal = "Decision Support Systems", volume = "20", issue = "2", publisher = "Elsevier Science", pages = "165-184", year = "1997", abstract="Valuation-based systems (VBS) provide a general framework for representing knowledge and drawing inferences under uncertainty. Recent studies have shown that the VBS can also represent and solve Bayesian decision problems. This paper proposes a decision calculus for belief function theory in the VBS. The proposed calculus uses a parameter whose role is the probabilistic interpretation of an assumption that disambiguates decision problems represented with belief functions. We show that the decision problems can be solved by using local computations with the presented calculus if they are represented in the VBS properly. We also show that the presented calculus can be reduced to the one for Bayesian decision problems when probabilities, instead of belief functions, are given." } @article{xu96decision, author = "Hong Xu and Yen-Teh Hsia and Philippe Smets", title = "The Transferable Belief Model for Decision Making in the Valuation-Based Systems", journal= "IEEE Transactions on Systems, Man, and Cybernetics", volume = "26A", pages = "698-707", year = "1996" } @article{schubert95onrho, author = "Johan Schubert", title = "On \'rho\' in a Decision-Theoretic Apparatus of {D}empster-{S}hafer Theory", journal = "International Journal of Approximate Reasoning", volume = "13", issue = "3", publisher = "Elsevier Science", pages = "185-200", year = "1995", abstract="Thomas M. Strat has developed a decision-theoretic apparatus for Dempster-Shafer theory (Decision analysis using belief functions, Intern. J. Approx. Reason. 4(5/6), 391-417, 1990). In this apparatus, expected utility intervals are constructed for different choices. The choice with the highest expected utility is preferable to others. However, to find the preferred choice when the expected utility interval of one choice is included in that of another, it is necessary to interpolate a discerning point in the intervals. This is done by the parameter «rho», defined as the probability that the ambiguity about the utility of every nonsingleton focal element will turn out as favorable as possible. If there are several different decision makers, we might sometimes be more interested in having the highest expected utility among the decision makers rather than only trying to maximize our own expected utility regardless of choices made by other decision makers. The preference of each choice is then determined by the probability of yielding the highest expected utility. This probability is equal to the maximal interval length of «rho» under which an alternative is preferred. We must here take into account not only the choices already made by other decision makers but also the rational choices we can assume to be made by later decision makers. In Strats apparatus, an assumption, unwarranted by the evidence at hand, has to be made about the value of «rho». We demonstrate that no such assumption is necessary. It is sufficient to assume a uniform probability distribution for «rho» to be able to discern the most preferable choice. We discuss when this approach is justifiable." } @article{bauer97approximation, author = "M. Bauer", title = "Approximation algorithms and decision making in the {D}empster-{S}hafer theory of evidence -- {A}n empirical study", journal = "International Journal of Approximate Reasoning", volume = "17", issue = "2--3", publisher = "Elsevier Science", pages = "217--237", year = "1997"} @article{binaghi99fuzzy, author = "Elisabetta Binaghi and Paolo Madella", title = "Fuzzy {D}empster-{S}hafer reasoning for rule-based classifiers", journal = "International Journal of Intelligent Systems", volume = "14", issue = "6", publisher = "John Wiley and Sons", pages = "559-583", year = "1999", abstract="In real classification problems intrinsically vague information often coexist with conditions of `lack of specificity' originating from evidence not strong enough to induce knowledge, but only degrees of belief or credibility regarding class assignments. The problem has been addressed here by proposing a fuzzy Dempster-Shafer model (FDS) for multisource classification purposes. The salient aspect of the work is the definition of an empirical learning strategy for the automatic generation of fuzzy Dempster-Shafer classification rules from a set of exemplified training data. Dempster-Shafer measures of uncertainty are semantically related to conditions of ambiguity among the data and then automatically set during the learning process. Partial reduced beliefs in class assignments are then induced and explicitly represented when generating classification rules. The fuzzy deductive apparatus has been modified and extended to integrate the Dempster-Shafer propagation of evidence. The strategy has been applied to a standard classification problem in order to develop a sensitivity analysis in an easily controlled domain. A second experimental test has been conducted in the field of natural risk assessment, where vagueness and lack of specificity conditions are prevalent. These empirical tests show that classification benefits from the combination of the fuzzy and Dempster-Shafer models especially when conditions of lack of specifity among data are prevalent. " } @article{fixsen97modified, author = "Dale Fixsen and Ronald P.S. Mahler", title = "Modified {D}empster-{S}hafer approach to classification", journal = "IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans.", volume = "27", issue = "1", publisher = "IEEE", pages = "96-104", year = "1997", abstract="This paper describes `modified Dempster-Shafer' (MDS), an approach to object identification which incorporates Bayesian prior distributions into an altered Dempster-Shafer rule of combination. The MDS combination rule reduces, under strong independence assumptions, to a special case of Bayes' rule. We show that MDS has rigorous probabilistic foundations in the theory of random sets. We also demonstrate close relationships between MDS and Smets' `pignistic' probabilities, which in the MDS framework become true posterior distributions. We describe the application of MDS to a practical classification algorithm which uses an information-theoretic technique to limit the combinatorial explosion of evidence. We also define a non-ad hoc, MDS-based classification `miss distance' metric used to measure the performance of this algorithm. " } @inproceedings{Xu93a, author = "Hong Xu and Y.T. Hsia and Philippe Smets", title = "A Belief-Function Based Decision Support System", booktitle= "Proceedings of the 9th Uncertainty in Artificial Intelligence", editor = "Heckerman D. and Mamdani A", journal= "", volume = "", pages = "535-542", year = "1993" } @inproceedings{Xu92a, author = "Hong Xu", title = "A Decision Calculus for Belief Functions in Valuation-Based Systems", booktitle= "Proceedings of the 8th Uncertainty in Artificial Intelligence", editor = "Dubois D. Wellman M. P. D\'Ambrosio B. and Smets Ph.", journal= "", volume = "", pages = "352-359", year = "1992" } @inproceedings{schubert97creating, author = "Johan Schubert", title = "Creating Prototypes for Fast Classification in {D}empster-{S}hafer Clustering", booktitle= "Proceedings of the International Joint Conference on Qualitative and Quantitative Practical Reasoning (ECSQARU / FAPR '97)", editor = "", journal= "", volume = "", pages = "", year = "Bad Honnef, Germany, 9-12 June 1997" } %% computer vision appl. @article{horiuchi98decision, author = "Takahiko Horiuchi", title = "Decision rule for pattern classification by integrating interval feature values", journal = "IEEE Transactions on Pattern Analysis and Machine Intelligence", volume = "20", issue = "4", publisher = "IEEE", pages = "440-448", year = "1998", abstract="Pattern classification based on Bayesian statistical decision theory needs a complete knowledge of the probability laws to perform the classification. In the actual pattern classification, however, it is generally impossible to get the complete knowledge as constant feature values by the influence of noise. Therefore, it is necessary to construct more flexible and robust theory for pattern classification. In this paper, a pattern classification theory using feature values defined on closed interval is formalized in the framework of Dempster-Shafer measure. Then, in order to make up lacked information, an integration algorithm is proposed, which integrates information observed by several information sources with considering source values. " } @article{mascle98introduction, author = "S. Le H\'egarat-Mascle, I. Bloch and D. Vidal-Madjar", title = "Introduction of neighborhood information in evidence theory and application to data fusion of radar and optical images with partial cloud cover", journal = "Pattern Recognition", volume = "31", issue = "11", publisher = "Elsevier Science", pages = "1811-1823", year = "1998", abstract="Two ways of introducing spatial information in Dempster-Shafer evidence theory are examined: in the definition of the monosource mass functions, and, during data fusion. In the latter case, a neighborhood mass function is derived from the label image and combined with the radiometric masses, according to the Dempster orthogonal sum. The main advantage of such a combination law is to adapt the importance of neighborhood information to the level of radiometric missing information. The importance of introducing neighborhood information has been illustrated through the following application: forest area detection using radar and optical images showing a partial cloud cover." } @article{ng98equalisation, author = "See Ng Geok and Singh Harcharan", title = "Data equalisation with evidence combination for pattern recognition", journal = "Pattern Recognition Letters", volume = "19", issue = "3-4", publisher = "Elsevier Science", pages = "227-235", year = "1998" } @article{boshra99accommodating, author = "Michael Boshra and Hong Zhang", title = "Accommodating uncertainty in pixel-based verification of 3-D object hypotheses", journal = "Pattern Recognition Letters", volume = "20", issue = "7", publisher = "Elsevier Science", pages = "689-698", year = "1999", abstract="We present a novel technique for verifying 3-D object hypotheses using an intensity image. Verification is performed through pixel-wise comparison of edge images corresponding to scene data and hypothesized model object. We accommodate the uncertainties involved in this process, which correspond to bounded positional errors of scene and model edge pixels, by dilating the scene edge image. An analytical framework is presented for formally determining the extent of dilation under the perspective projection. Performance of the technique is demonstrated using real and synthetic data." } @article{pinz96active, author = "Axel Pinz and Manfred Prantl and Harald Ganster and Hermann Kopp-Borotschnig", title = "Active fusion - A new method applied to remote sensing image interpretation", journal = "Pattern Recognition Letters", volume = "17", issue = "13", publisher = "Elsevier Science", pages = "1349-1359", year = "1996", abstract="Today's computer vision applications often have to deal with multiple, uncertain and incomplete visual information. In this paper, we introduce a new method, termed active fusion, which provides a common framework for active selection and combination of information from multiple sources in order to arrive at a reliable result at reasonable costs. The implementation of active fusion on the basis of probability theory, the Dempster-Shafer theory of evidence and fuzzy sets is discussed. In a sample experiment, active fusion using Bayesian networks is applied to agricultural field classification from multitemporal Landsat imagery. This experiment shows a significant reduction of the number of information sources required for a reliable decision." } @article{bloch96aspects, author = "Isabelle Bloch", title = "Some aspects of {D}empster-{S}hafer evidence theory for classification of multi-modality medical images taking partial volume effect into account", journal = "Pattern Recognition Letters", volume = "17", issue = "8", publisher = "Elsevier Science", pages = "905-919", year = "1996", abstract="This paper points out some key features of Dempster-Shafer evidence theory for data fusion in medical imaging. Examples are provided to show its ability to take into account a large variety of situations, which actually often occur and are not always well managed by classical approaches nor by previous applications of Dempster-Shafer theory in medical imaging. The modelization of both uncertainty and imprecision, the introduction of possible partial or global ignorance, the computation of conflict between images, the possible introduction of a priori information are all powerful aspects of this theory, which deserve to be more exploited in medical image processing. They may be of great influence on the final decision. They are illustrated on a simple example for classifying brain tissues in pathological dual echo MR images. In particular, partial volume effect can be properly managed by this approach." } @article{vasseur99perceptual, author = "P. Vasseur and C. Pegard and E. Mouaddib and L. Delahoche", title = "Perceptual organization approach based on {D}empster-{S}hafer theory", journal = "Pattern Recognition", volume = "32", issue = "8", publisher = "Elsevier Science", pages = "1449-1462", year = "1999", abstract="In this paper, we propose an application of the perceptual organization based on the Dempster-Shafer theory. This method is divided into two parts which respectively rectifies the segmentation mistakes by restoring the coherence of the segments and detects objects in the scene by forming groups of primitives. We show how we apply the Dempster-Shafer theory, usually used in data fusion, in order to obtain an optimal adequation between the perceptual organization problem and this tool. We show that without any prior knowledge and any threshold, our bottom-up algorithm detects efficiently the different objects even in cluttered environment. Moreover, we demonstrate its robustness and flexibility on indoor and outdoor scenes without any modification of parameters." } %% theory of capacities @techreport{benferhat95tech, author = "S. Benferhat and Alessandro Saffiotti and Philippe Smets", title = "Belief functions and default reasonings", institution = "Universite' Libre de Bruxelles, Technical Report TR/IRIDIA/95-5", year = "1995", } @article{bergsten93dempster, author = "Ulla Bergsten and Johan Schubert", title = "Dempster's Rule for Evidence Ordered in a Complete Directed Acyclic Graph", journal= "International Journal of Approximate Reasoning", volume = "9", pages = "37-73", year = "1993" } @article{schubert96specifying, author = "Johan Schubert", title = "Specifying Nonspecific Evidence", journal= "International Journal of Intelligent Systems", volume = "11", pages = "525-563", year = "1996" } @incollection{schubert99fast, author = "Johan Schubert", title = "Fast {D}empster-{S}hafer Clustering Using a Neural Network Structure", booktitle= "Information, Uncertainty and Fusion", editor = "B. Bouchon-Meunier, R. R. Yager and L. A. Zadeh", pages = "419-430", publisher= "Kluwer Academic Publishers (SECS 516), Boston, MA", year = "1999" } @article{smets93belief, author = "Philippe Smets", title = "Belief Functions : the Disjunctive Rule of Combination and the Generalized {B}ayesian Theorem", journal= "International Journal of Approximate Reasoning", volume = "9", pages = "1-35", year = "1993" } @incollection{smets95nonstandard, author = "Philippe Smets", title = "Non Standard Probabilistic and Non Probabilistic Representations of Uncertainty", booktitle= "Advances in Fuzzy Sets Theory and Technology, 3", editor = "Wang P.P.", pages = "125-154", publisher= "Duke University, Durham, NC", year = "1995" } @incollection{smets90constructing, author = "Philippe Smets", title = "Constructing the pignistic probability function in a context of uncertainty", booktitle= "Uncertainty in Artificial Intelligence, 5", editor = "M. Henrion and R.D. Shachter and L.N. Kanal and J.F. Lemmer", pages = "29-39", publisher= "Elsevier Science Publishers", year = "1990" } @incollection{smets99practical, author = "Philippe Smets", title = "Practical Uses of Belief Functions", booktitle= "Uncertainty in Artificial Intelligence 15", editor = "Laskey K. B. and Prade H.", pages = "612-621", publisher= "", year = "1999" } @incollection{smets98which, author = "Philippe Smets", title = "Probability, Possibility, Belief: Which and Where ?", booktitle= "Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 1: Quantified Representation of Uncertainty and Imprecision", editor = "Gabbay D. and Smets Ph.", pages = "1-24", publisher= "Kluwer, Doordrecht", year = "1998" } @incollection{smets98quantified, author = "Philippe Smets", title = "The Transferable Belief Model for Quantified Belief Representation", booktitle= "Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 1: Quantified Representation of Uncertainty and Imprecision", editor = "Gabbay D. and Smets Ph.", pages = "267-301", publisher= "Kluwer, Doordrecht", year = "1998" } @incollection{smets97TBMbelief, author = "Philippe Smets and R. Kruse", title = "The Transferable Belief Model for Belief Representation", booktitle= "Uncertainty Management in information systems: from needs to solutions", editor = "Motro A. and Smets Ph.", pages = "343-368", publisher= "Kluwer, Boston", year = "1997" } @article{smets92TBMrandom, author = "Philippe Smets", title = "The Transferable Belief Model and Random Sets", journal= "International Journal of Intelligent Systems", volume = "7", pages = "37-46", year = "1992" } @inproceedings{yagernonmonotonicity, author = "Ronald R. Yager", title = "Nonmonotonicity and Compatibility Relations in Belief Structures", booktitle= "", editor = "", journal= "", volume = "", pages = "", year = "" } @incollection{smets94what, author = "Philippe Smets", title = "What is {D}empster-{S}hafer's model ?", booktitle= "Advances in the Dempster-Shafer Theory of Evidence", editor = "Yager R.R., Fedrizzi M. and Kacprzyk J.", pages = "5-34", publisher= "Wiley", year = "1994" } @inproceedings{smets84fusion, author = "Philippe Smets", title = "Data Fusion in the Transferable Belief Model", booktitle= "Proceedings of the 1984 American Control Conference", editor = "", journal= "", volume = "", pages = "554-555", year = "1984" } @inproceedings{smets91updating, author = "Philippe Smets", title = "About Updating", booktitle= "Proceedings of the 7th conference on Uncertainty in Artificial Intelligence", editor = "D\'ambrosio, B. and Smets, Ph. and and, Bonissone P. P.", journal= "", volume = "", pages = "378-385", year = "1991" } @inproceedings{klawonn92dynamic, author = "F. Klawonn and Philippe Smets", title = "The Dynamic of Belief in the Transferable Belief Model and Specialization-Generalization Matrices", booktitle= "Proceedings of the 8th Conference on Uncertainty in Artificial Intelligence", editor = "Dubois D., Wellman M.P., D\'Ambrosio B. and Smets Ph.", journal= "", volume = "", pages = "130-137", year = "1992" } @inproceedings{smets92concept, author = "Philippe Smets", title = "The Concept of Distinct Evidence", booktitle= "Proceedings of the 4th Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 92)", editor = "", journal= "", volume = "", pages = "789-794", year = "Palma de Mallorca, 6-10 July 92" } @inproceedings{smets93jeffrey, author = "Philippe Smets", title = "Jeffrey's rule of conditioning generalized to belief functions", booktitle= "Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence (UAI93)", editor = "Heckerman D., Mamdani A.", journal= "", volume = "", pages = "500-505", year = "1993" } @inproceedings{smets93quantifying, author = "Philippe Smets", title = "Quantifying Beliefs by Belief Functions : An Axiomatic Justification", booktitle= "Proceedings of the 13th International Joint Conference on Artificial Intelligence, IJCAI93", editor = "", journal= "", volume = "", pages = "598-603", year = "1993" } @techreport{smets95axiomatic, author = "Philippe Smets", title = "The Axiomatic Justification of the Transferable Belief Model", institution = "Universite' Libre de Bruxelles, Technical Report TR/IRIDIA/1995-8.1", year = "1995", } @techreport{smets90nonmonotonic, author = "Y.T. Hsia and Ph. Smets", title = "Belief Functions and non-monotonic reasoning", institution = "Universit\'e Libre de Bruxelles, Technical Report IRIDIA/TR/1990/3", year = "1990", } @techreport{smets90defeasible, author = "Philippe Smets and Yen-Teh Hsia", title = "Defeasible Reasoning with Belief Functions", institution = "Universite' Libre de Bruxelles, Technical Report TR/IRIDIA/90-9", year = "1990", } @inproceedings{smets86bayes, author = "Philippe Smets", title = "Bayes' theorem generalized for belief functions", booktitle= "Proceedings of ECAI-86", editor = "", journal= "", volume = "2", pages = "169-171", year = "1986" } @inproceedings{smets87bayes, author = "Philippe Smets", title = "Belief functions and generalized {B}ayes theorem", booktitle= "Proceedings of the Second IFSA Congress", editor = "", journal= "", volume = "", pages = "404-407", year = "Tokyo, Japan, 1987" } @inproceedings{smets92nature, author = "Philippe Smets", title = "The nature of the unnormalized beliefs encountered in the transferable belief model", booktitle= "Proceedings of the 8th Conference on Uncertainty in Artificial Intelligence (AI92)", editor = "Dubois D., Wellmann M.P., D\'Ambrosio B. and Smets Ph.", journal= "", volume = "", pages = "292-297", year = "1992" } @article{nguyen93dynamics, author = "H. T. Nguyen and Philippe Smets", title = "On Dynamics of Cautious Belief and Conditional Objects", journal= "International Journal of Approximate Reasoning", volume = "8", pages = "89-104", year = "1993" } @inproceedings{smets94knowledge, author = "Philippe Smets", title = "Belief induced by the Knowledge of some Probabilities", booktitle= "Proceedings of the 10th Conference on Uncertainty in Artificial Intelligence (AI94)", editor = "Heckerman D., Poole D., Lopez de Mantaras R.", journal= "", volume = "", pages = "523-530", year = "1994" } @incollection{smets79medical, author = "Ph. Smets", title = "Medical diagnosis : {F}uzzy sets and degree of belief", booktitle = "Proceedings of MIC'79", editor = "J. Willems", pages = "185--189", publisher= "Wiley", year = "1979" } @article{smets81medical, author = "Ph. Smets", title = "Medical Diagnosis : Fuzzy Sets and Degrees of Belief", journal= "Int. J. Fuzzy Sets and systems", volume = "5", pages = "259-266", year = "1981" } @article{smets98application, author = "Philippe Smets", title = "The Application of the Transferable Belief Model to Diagnostic Problems", journal= "Int. J. Intelligent Systems", volume = "13", pages = "127-158", year = "1998" } @article{smets92reliability, author = "Philippe Smets", title = "The Transferable Belief Model for Expert Judgments and Reliability Problems", journal= "Reliability Engineering and System Safety", volume = "38", pages = "59-66", year = "1992" } @article{ayoun01data, author = "A. Ayoun and Philippe Smets.", title = "Data association in multi-target detection using the transferable belief model", journal= "Intern. J. Intell. Systems", volume = "", pages = "", year = "2001" } @incollection{smets91default, author = "Philippe Smets and Y. T. Hsia", title = "Default Reasoning and the Transferable Belief Model", booktitle= "Uncertainty in Artificial Intelligence 6", editor = "P.P. Bonissone and M. Henrion and L.N. Kanal and J.F. Lemmer", pages = "495-504", publisher= "Wiley", year = "1991" } @incollection{smets01decision, author = "Philippe Smets", title = "Decision Making in a Context where Uncertainty is Represented by Belief Functions", booktitle= "Belief Functions in Business Decisions", editor = "Srivastava R.", pages = "495-504", publisher= "Physica-Verlag", year = "2001" } @inproceedings{smets93nodutch, author = "Philippe Smets", title = "No {D}utch {B}ook can be built against the {TBM} even though update is not obtained by {B}ayes rule of conditioning", booktitle= "SIS, Workshop on Probabilistic Expert Systems", editor = "R. Scozzafava", journal= "", volume = "", pages = "181-204", year = "Roma, Italy, 1993" } @inproceedings{elouedi00decision, author = "Z. Elouedi and K. Mellouli and Philippe Smets", title = "Decision trees using belief function theory", booktitle= "Proceedings of the Eighth International Conference IPMU: Information Processing and Management of Uncertainty in Knowledge-based Systems", editor = "", journal= "", volume = "1", pages = "141-148", year = "Madrid, 2000" } @inproceedings{elouedi00classification, author = "Z. Elouedi and K. Mellouli and Philippe Smets", title = "Classification with Belief Decision Trees", booktitle= "Proceedings of the Nineth International Conference on Artificial Intelligence: Methodology, Systems, Architectures: AIMSA 2000", editor = "", journal= "", volume = "", pages = "", year = "Varna, Bulgaria, 2000" } @incollection{kennes91fast, author = "R. Kennes and Philippe Smets", title = "Fast algorithms for {D}empster-{S}hafer theory", booktitle= "Uncertainty in Knowledge Bases, Lecture Notes in Computer Science 521", editor = "B. Bouchon-Meunier, R.R. Yager, L.A. Zadeh", pages = "14-23", publisher= "Springer-Verlag, Berlin", year = "1991" } @incollection{kennes91computational, author = "R. Kennes and Philippe Smets", title = "Computational Aspects of the Moebius Transformation", booktitle= "Uncertainty in Artificial Intelligence 6", editor = "P.P. Bonissone and M. Henrion and L.N. Kanal and J.F. Lemmer", pages = "401-416", publisher= "Elsevier Science Publishers", year = "1991" } @inproceedings{smets87versus, author = "Philippe Smets", title = "Upper and lower probability functions versus belief functions", booktitle= "Proceedings of the International Symposium on Fuzzy Systems and Knowledge Engineering", editor = "", journal= "", volume = "", pages = "17-21", year = "Guangzhou, China, 1987" } @incollection{smets88beliefversus, author = "Philippe Smets", title = "Belief functions versus probability functions", booktitle= "Uncertainty and Intelligent Systems", editor = "Bouchon B., Saitta L. and Yager R.", pages = "17-24", publisher= "Springer Verlag, Berlin", year = "1988" } @inproceedings{smets88versus, author = "Philippe Smets", title = "Transferable belief model versus {B}ayesian model", booktitle= "Proceedings of ECAI 1988", editor = "Kodratoff Y.", journal= "", volume = "", pages = "495-500", year = "Pitman, London, 1988" } @inproceedings{smets90possibility, author = "Philippe Smets", title = "The transferable belief model and possibility theory", booktitle= "Proceedings of NAFIPS-90", editor = "Kodratoff Y.", journal= "", volume = "", pages = "215-218", year = "1990" } @incollection{smets95what, author = "Philippe Smets", title = "Probability, Possibility, Belief : which for what ?", booktitle= "Foundations and Applications of Possibility Theory", editor = "De Cooman G., Ruan D., Kerre E.E.", pages = "20-40", publisher= "World Scientific, Singapore", year = "1995" } @incollection{smets98numerical, author = "Philippe Smets", title = "Numerical Representation of Uncertainty", booktitle= "Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 3: Belief Change", editor = "Gabbay D. and Smets Ph. (Series Eds). Dubois D. and Prade H. (Vol. Eds.)", pages = "265-309", publisher= "Kluwer, Doordrecht", year = "1998" } @inproceedings{schubert99simultaneous, author = "Johan Schubert", title = "Simultaneous {D}empster-{S}hafer clustering and gradual determination of number of clusters using a neural network structure", booktitle= "Proceedings of the 1999 Information, Decision and Control Conference (IDC'99)", editor = "", journal= "", volume = "", pages = "401-406", year = "Adelaide, Australia, 8-10 February 1999" } @inproceedings{schubert98neural, author = "Johan Schubert", title = "A neural network and iterative optimization hybrid for {D}empster-{S}hafer clustering", booktitle= "Proceedings of EuroFusion98 International Conference on Data Fusion (EF'98)", editor = "M. Bedworth, J. O'Brien", journal= "", volume = "", pages = "29-36", year = "Great Malvern, UK, 6-7 October 1998" } @inproceedings{schubert98fast, author = "Johan Schubert", title = "Fast {D}empster-{S}hafer clustering using a neural network structure", booktitle= "Proceedings of the Seventh International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU'98)", editor = "", journal= "", volume = "", pages = "1438-1445", year = "Universit\'e de La Sorbonne, Paris, France, 6-10 July 1998" } @inproceedings{bergsten97applying, author = "Ulla Bergsten and Johan Schubert and P. Svensson", title = "Applying Data Mining and Machine Learning Techniques to Submarine Intelligence Analysise", booktitle= "Proceedings of the Third International Conference on Knowledge Discovery and Data Mining (KDD'97)", editor = "D. Heckerman and H. Mannila and D. Pregibon and R. Uthurusamy", journal= "", volume = "", pages = "127-130", year = "Newport Beach, USA, 14-17 August 1997" } @article{schubert95cluster, author = "Johan Schubert", title = "Cluster-based Specification Techniques in {D}empster-{S}hafer Theory for an Evidential Intelligence Analysis of MultipleTarget Tracks", journal= "AI Communications", volume = "8:2", pages = "107-110", year = "1995" } @article{schubert95finding, author = "Johan Schubert", title = "Finding a Posterior Domain Probability Distribution by Specifying Nonspecific Evidence", journal= "International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems", volume = "3:2", pages = "163-185", year = "1995" } @PHDTHESIS{schubert94thesis, author = "Johan Schubert", title = "Cluster-based Specification Techniques in {D}empster-{S}hafer Theory for an Evidential Intelligence Analysis of MultipleTarget Tracks", school = "Royal Institute of Technology, Sweden", type = "{PhD} Dissertation", address = "", month = "", year = 1994, note = "", } @article{schubert93nonspecific, author = "Johan Schubert", title = "On Nonspecific Evidence", journal= "International Journal of Intelligent Systems", volume = "8:6", pages = "711-725", year = "1993" } @BOOK{buchanan1984, author = {B. 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Hajek", title = "Deriving {D}empster's rule", booktitle= "Proceeding of IPMU'92", editor = "", journal= "", volume = "", pages = "73-75", year = "1992" } @inproceedings{wilson93pignistic, author = "Nic Wilson", title = "Decision making with belief functions and pignistic probabilities", booktitle= "Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty", editor = "", journal= "", volume = "", pages = "364-371", year = "Granada, 1993" } @inproceedings{yaghlane00independence, author = "B. Ben Yaghlane and Philippe Smets and K. Mellouli", title = "Independence concepts for belief functions", booktitle= "Proceedings of Information Processing and Management of Uncertainty (IPMU'2000)", editor = "", journal= "", volume = "", pages = "", year = "2000" } @inproceedings{denoeux95neural, author = "Thierry Denoeux", title = "An evidence-theoretic neural network classifier", booktitle= "Proceedings of the 1995 IEEE International Conference on Systems, Man, and Cybernetics (SMC'95)", editor = "", journal= "", volume = "3", pages = "712-717", year = "October 1995" } @article{vorbraak89efficient, author = "F. Vorbraak", title = "A computationally efficient approximation of {D}empster-{S}hafer theory", journal= "International Journal on Man-Machine Studies", volume = "30", pages = "525-536", year = "1989" } @article{hummel88statistical, author = "R. Hummel and M. 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Brahm", title = "Using {D}empster-{S}hafer methods for object classification in the theater ballistic missile environment", booktitle= "Proceedings of the SPIE - Sensor Fusion: Architectures, Algorithms, and Applications III", editor = "", journal= "", volume = "3719", pages = "103-113", year = "Orlando, FL, USA, 7-9 April 1999" } @article{filippidis99comparison, author = "A. Filippidis", title = "A comparison of fuzzy and {D}empster-{S}hafer evidential reasoning fusion methods for deriving course of action from surveillance observations", journal= "International Journal of Knowledge-Based Intelligent Engineering Systems", volume = "3:4", pages = "215-222", year = "October 1999" } @article{lowrance88automated, author = "John D. Lowrance", title = "Automated argument construction", journal= "Journal of Statistical Planning Inference", volume = "20", pages = "369-387", year = "1988" } @inproceedings{binaghi98neural, author = "Elisabetta Binaghi and P. Madella and I. Gallo and A. Rampini", title = "A neural refinement strategy for a fuzzy {D}empster-{S}hafer classifier of multisource remote sensing images", booktitle= "Proceedings of the SPIE - Image and Signal Processing for Remote Sensing IV", editor = "", journal= "", volume = "3500", pages = "214-224", year = "Barcelona, Spain, 21-23 Sept. 1998" } @inproceedings{markakis98boolean, author = "G. Markakis", title = "A boolean generalization of the {D}empster-{S}hafer construction of belief and plausibility functions", booktitle= "Proceedings of the Fourth International Conference on Fuzzy Sets Theory and Its Applications", editor = "", journal= "", volume = "", pages = "117-125", year = "Liptovsky Jan, Slovakia, 2-6 Feb. 1998" } @inproceedings{straszecka98on, author = "E. Straszecka", title = "On an application of {D}empster-{S}hafer theory to medical diagnosis support", booktitle= "Proceedings of the 6th European Congress on Intelligent Techniques and Soft Computing (EUFIT'98)", editor = "", journal= "", volume = "3", pages = "1848-1852", year = "Aachen, Germany: Verlag Mainz, 1998" } @inproceedings{lee00protection, author = "Seung-Jae Lee and Sang-Hee Kang and Myeon-Song Choi and Sang-Tae Kim and Choong-Koo Chang", title = "Protection level evaluation of distribution systems based on {D}empster-{S}hafer theory of evidence", booktitle= "Proceedings of the IEEE Power Engineering Society Winter Meeting", editor = "", journal= "", volume = "3", pages = "1894-1899", year = "Singapore, 23-27 January 2000" } @inproceedings{pieczynski00unsupervised, author = "W. Pieczynski", title = "Unsupervised {D}empster-{S}hafer fusion of dependent sensors", booktitle= "Proceedings of the 4th IEEE Southwest Symposium on Image Analysis and Interpretation", editor = "", journal= "", volume = "", pages = "247-251", year = "Austin, TX, USA, 2-4 April 2000" } @inproceedings{korpisaari99dempster, author = "P. Korpisaari and J. Saarinen", title = "Dempster-{S}hafer belief propagation in attribute fusion", booktitle= "Proceedings of the Second International Conference on Information Fusion (FUSION'99)", editor = "", journal= "", volume = "2", pages = "1285-1291", year = "Sunnyvale, CA, USA, 6-8 July 1999" } @inproceedings{sosnowski99generating, author = "Z. A. Sosnowski and J. S. Walijewski", title = "Generating fuzzy decision rules with the use of {D}empster-{S}hafer theory", booktitle= "Proceedings of the 13th European Simulation Multiconference 1999", editor = "Szczerbicka, H.", journal= "", volume = "2", pages = "419-426", year = "Warsaw, Poland, 1-4 June 1999" } % evidential model - bibtex inproceedings{1068941, author = {Cristian Sminchisescu and Atul Kanaujia and Zhiguo Li and Dimitris Metaxas}, title = {Discriminative Density Propagation for 3D Human Motion Estimation}, booktitle = {CVPR '05: Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1}, year = {2005}, isbn = {0-7695-2372-2}, pages = {390--397}, doi = {http://dx.doi.org/10.1109/CVPR.2005.132}, publisher = {IEEE Computer Society}, address = {Washington, DC, USA}, } @inproceedings{bb71672, AUTHOR = "Rosales, R. and Siddiqui, M. and Alon, J. and Sclaroff, S.", TITLE = "Estimating 3D Body Pose using Uncalibrated Cameras", BOOKTITLE = CVPR01, YEAR = "2001", PAGES = "I:821-827", BIBSOURCE = "http://www.visionbib.com/bibliography/people923.html#TT68310"} @inproceedings{bb71588, AUTHOR = "Howe, N.R.", TITLE = "Silhouette Lookup for Automatic Pose Tracking", BOOKTITLE = Non-Rigid04, YEAR = "2004", PAGES = "15", BIBSOURCE = "http://www.visionbib.com/bibliography/people923.html#TT68230"} @inproceedings{bb71655, AUTHOR = "Grauman, K. and Shakhnarovich, G. and Darrell, T.J.", TITLE = "Inferring 3D Structure with a Statistical Image-Based Shape Model", BOOKTITLE = ICCV03, YEAR = "2003", PAGES = "641-648", BIBSOURCE = "http://www.visionbib.com/bibliography/people923.html#TT68296"} @inproceedings{bb71611, AUTHOR = "Elgammal, A.M. and Lee, C.S.", TITLE = "Inferring 3D body pose from silhouettes using activity manifold learning", BOOKTITLE = CVPR04, YEAR = "2004", PAGES = "II: 681-688", BIBSOURCE = "http://www.visionbib.com/bibliography/people923.html#TT68252"} @inproceedings{bb70669, AUTHOR = "Okada, K. and von der Malsburg, C.", TITLE = "Pose-invariant face recognition with parametric linear subspaces", BOOKTITLE = AFGR02, YEAR = "2002", PAGES = "64-69", BIBSOURCE = "http://www.visionbib.com/bibliography/people913.html#TT67324"} @inproceedings{niyogi96afgr, AUTHOR = "Niyogi, S. and Freeman, W.T.", TITLE = "Example-based head tracking", BOOKTITLE = "Proceedings of the Second International Conference on Automatic Face and Gesture Recognition", YEAR = "1996", PAGES = "374--378" } @inproceedings{1015343, author = {Ankur Agarwal and Bill Triggs}, title = {Learning to track 3D human motion from silhouettes}, booktitle = {ICML '04: Proceedings of the twenty-first international conference on Machine learning}, year = {2004}, isbn = {1-58113-828-5}, pages = {2}, location = {Banff, Alberta, Canada}, doi = {http://doi.acm.org/10.1145/1015330.1015343}, publisher = {ACM Press}, address = {New York, NY, USA}, } @article{10.1109/CVPR.2004.5, author = {Ankur Agarwal and Bill Triggs}, title = {3D Human Pose from Silhouettes by Relevance Vector Regression}, journal = {cvpr}, volume = {02}, year = {2004}, issn = {1063-6919}, pages = {882-888}, doi = {http://doi.ieeecomputersociety.org/10.1109/CVPR.2004.5}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } @inproceedings{bb33622, AUTHOR = "Zheng, Y. and Zhou, X.S. and Georgescu, B. and Zhou, S.K. and Comaniciu, D.", TITLE = "Example Based Non-rigid Shape Detection", BOOKTITLE = ECCV06, YEAR = "2006", PAGES = "IV: 423-436", BIBSOURCE = "http://www.visionbib.com/bibliography/describe468.html#TT31863"} @inproceedings{796041, author = {Thomas Maurer and Christoph von der Malsburg}, title = {Tracking and Learning Graphs and Pose on Image Sequences of Faces}, booktitle = {FG '96: Proceedings of the 2nd International Conference on Automatic Face and Gesture Recognition (FG '96)}, year = {1996}, isbn = {0-8186-7713-9}, pages = {76}, publisher = {IEEE Computer Society}, address = {Washington, DC, USA}, } @inproceedings{bb71628, AUTHOR = "Poppe, R. and Poel, M.", TITLE = "Comparison of Silhouette Shape Descriptors for Example-based Human Pose Recovery", BOOKTITLE = FGR06, YEAR = "2006", PAGES = "541-546", BIBSOURCE = "http://www.visionbib.com/bibliography/people923.html#TT68269"} @article{1248700, author = {Margarita Osadchy and Yann Le Cun and Matthew L. Miller}, title = {Synergistic Face Detection and Pose Estimation with Energy-Based Models}, journal = {J. Mach. Learn. Res.}, volume = {8}, year = {2007}, issn = {1533-7928}, pages = {1197--1215}, publisher = {MIT Press}, address = {Cambridge, MA, USA}, } @inproceedings{1099953, author = {Tai-Peng Tian and Rui Li and Stan Sclaroff}, title = {Articulated Pose Estimation in a Learned Smooth Space of Feasible Solutions}, booktitle = {CVPR '05: Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Workshops}, year = {2005}, isbn = {0-7695-2372-2-3}, pages = {50}, doi = {http://dx.doi.org/10.1109/CVPR.2005.414}, publisher = {IEEE Computer Society}, address = {Washington, DC, USA}, } @inproceedings{946721, author = {Gregory Shakhnarovich and Paul Viola and Trevor Darrell}, title = {Fast Pose Estimation with Parameter-Sensitive Hashing}, booktitle = {ICCV '03: Proceedings of the Ninth IEEE International Conference on Computer Vision}, year = {2003}, isbn = {0-7695-1950-4}, pages = {750}, publisher = {IEEE Computer Society}, address = {Washington, DC, USA}, } @techreport{eemcs1881, number = {TR-CTIT-05-49}, howpublished = {http://eprints.eemcs.utwente.nl/1881/}, eprint_note = {Imported from HMI}, author = {R. W. Poppe and M. Poel}, type = {CTIT Technical Report series}, address = {Enschede}, title = {Example-based pose estimation in monocular images using compact fourier descriptors}, publisher = {Centre for Telematics and Information Technology, University of Twente}, year = {2005}, institution = {University of Twente}, research_groups = {EWI-HMI: Human Media Interaction}, refereed = {No}, eprintid = {1881}, research_projects = {AMI: Augmented Multi-party Interaction, ICIS: Interactive Collaborative Information Systems}, issn = {1381-3625}, num_pages = {19} } @INPROCEEDINGS{Poppe717:2007, author={R.W. Poppe}, title={Evaluating Example-based Pose Estimation: Experiments on the HumanEva Sets}, booktitle={Online Proceedings of the Workshop on Evaluation of Articulated Human Motion and Pose Estimation (EHuM) at the International Conference on Computer Vision and Pattern Recognition (CVPR)}, year=2007, pages={1--8}, address={Minnesota, Minneapolis}, month=jun, } @inproceedings{bb71629, AUTHOR = "Agarwal, A. and Triggs, B.", TITLE = "A Local Basis Representation for Estimating Human Pose from Cluttered Images", BOOKTITLE = ACCV06, YEAR = "2006", PAGES = "I:50-59", BIBSOURCE = "http://www.visionbib.com/bibliography/people923.html#TT68270"} @inproceedings{bb70706, AUTHOR = "Li, S.Z. and Fu, Q.D. and Gu, L. and Scholkopf, B. and Cheng, Y. and Zhang, H.J.", TITLE = "Kernel Machine Based Learning for Multi-View Face Detection and Pose Estimation", BOOKTITLE = ICCV01, YEAR = "2001", PAGES = "II: 674-679", BIBSOURCE = "http://www.visionbib.com/bibliography/people913.html#TT67361"} @misc{Hayashi06, author = "Kanako Hayashi and Lionel Heng and Vikram Srivastava", title = "Pose Estimation From Occluded Images", text = "CS 229 - Machine Learning Class Project. Stanford University, Computer Science department.", year = "2006" } % old stuff @misc{ jsang06normalising, author = "A. Jsang and S. Pope", title = "Normalising the Consensus Operator for Belief Fusion", text = "A. Jsang and S. Pope. Normalising the Consensus Operator for Belief Fusion. In Proceedings of the International Conference on Information Processing and Management of Uncertainty (IPMU2006), Paris, July 2006.", year = "2006" } @INPROCEEDINGS{2004SPIE.5429..392S, author = {{Sun}, H. and {Farooq}, M.}, title = "{Conjunctive and disjunctive combination rules of evidence}", booktitle = {Signal Processing, Sensor Fusion, and Target Recognition XIII. Edited by Kadar, Ivan. Proceedings of the SPIE, Volume 5429, pp. 392-401 (2004).}, year = 2004, editor = {{Kadar}, I.}, month = aug, pages = {392-401}, doi = {10.1117/12.544033}, adsurl = {http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2004SPIE.5429..392S&db_key=PHY}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} @misc{ordonez02frem, author = "C. Ordonez and E. Omiecinski", title = "FREM: Fast and robust EM clustering for large data sets", text = "C. Ordonez and E. Omiecinski. FREM: Fast and robust EM clustering for large data sets. In ACM CIKM Conference, 2002.", year = "2002", url = "citeseer.ist.psu.edu/ordonez02frem.html" } @inproceedings{moore-veryfast, Month = {April}, Year = {1999}, Pages = {543--549}, Publisher = {Morgan Kaufman}, Address = {340 Pine Street, 6th Fl., San Francisco, CA 94104}, Booktitle = {Advances in Neural Information Processing Systems}, Editor = {M. Kearns and D. Cohn}, Author = {Andrew Moore}, Title = {Very Fast EM-based Mixture Model Clustering Using Multiresolution KD-trees} } @book{McLachlan00book, author = "G. McLachlan and D. Peel", title = "Finite Mixture Models", publisher = "Wiley-Interscience", address= "", year = "2000" } @article{burman89cross, author = "P. Burman", title = "A comparative study of ordinary cross-validation, v-fold cross-validation and the repeated learning-testing methods", journal= "Biometrika", volume = "76(3)", pages = "503--514", year = "1989" } @article{denoeux01inner, author = "T. Denouex", title = "Inner and outer approximation of belief structures using a hierarchical clustering approach", journal= "International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems", volume = "9(4)", pages = "437--460", year = "2001" } @inproceedings{ristic04ipmu, author = {B. Ristic and P. Smets}, title = {Belief Function Theory on the Continuous Space with an Application to Model Based Classification}, booktitle = {IPMU}, year = {2004}, pages = {1119-1126} } @article{smets05ijar, author = "Ph. smets", title = "Decision making in the TBM: the necessity of the pignistic transformation", journal= "International Journal of Approximate Reasoning", volume = "38(2)", pages = "133--147", year = "February 2005" } @article{cobb06ijar, author = "B.R. Cobb and P.P. Shenoy", title = "On the plausibility transformation method for translating belief function models to probability models", journal= "International Journal of Approximate Reasoning", volume = "41(3)", pages = "314--330", year = "April 2006" } @techreport{Danieltech, author = "M. Daniel", title = "Transformations of belief functions to probabilities", institution = "Institute of Computer Science, Academy of Sciences of the Csech Republic", year = "", } @article{Haenni02ijar, author = "R. Haenni and N. Lehmann", title = "Resource bounded and anytime approximation of belief function computations", journal= "International Journal of Approximate Reasoning", volume = "31(1-2)", pages = "103-154", year = "October 2002" } @article{Denoeux02ijar, author = "T. Denoeux and A. Ben Yaghlane", title = "Approximating the Combination of Belief Functions using the Fast Moebius Transform in a coarsened frame", journal= "International Journal of Approximate Reasoning", volume = "31(1-2)", pages = "77-101", year = "October 2002" } @article{Denoeux01ijufk, author = "T. Denoeux", title = "Inner and outer approximation of belief structures using a hierarchical clustering approach", journal= "Int. Journal of Uncertainty, Fuzziness and Knowledge-Based Systems", volume = "9(4)", pages = "437-460", year = "2001" } @article{Cobb03isf, author = "B. R. Cobb and P. P. Shenoy", title = "A comparison of Bayesian and belief function reasoning", journal= "Information Systems Frontiers", volume = "5(4)", pages = "345-358", year = "2003" } @inproceedings{Cobb03ecsqaru, author = "B. R. Cobb and P. P. Shenoy", title = "A comparison of methods for transforming belief function models to probability models", booktitle= "Proceedings of ECSQARU'2003, Aalborg, Denmark", editor = "", journal= "", volume = "", pages = "255-266", year = "July 2003" } @inproceedings{Yaghlane01ecsqaru, author = "A. Ben Yaghlane and T. Denoeux and K. Mellouli", title = "Coarsening approximations of belief functions", booktitle= "Proceedings of ECSQARU'2001", editor = "S. Benferhat and P. Besnard", journal= "LNAI 2143", volume = "", pages = "362-373", year = "2001" } @inproceedings{cuzzolin05isipta, author = "F. Cuzzolin and R. Frezza", title = "Evidential modeling for pose estimation", booktitle= "accepted by the $4^{th}$ Interbational Symposium on Imprecise Probabilities and Their Applications (ISIPTA'05)", editor = "", journal= "", volume = "", pages = "", year = "July 2005" } @article{cuzzolin05amai, author = "F. Cuzzolin", title = "Algebraic structure of the families of compatible frames of discernment", journal= "Annals of Mathematics and Artificial Intelligence", volume = "45(1-2)", pages = "241-274", year = "2005" } @article{cuzzolin05smcc, author = "F. Cuzzolin", title = "Geometrical structure of belief space and conditional subspaces", journal = "submitted to the IEEE Transactions on Systems, Man and Cybernetics part C", volume = "", pages = "", year = "July 2005" } @article{cuzzolin06smcb, author = "F. Cuzzolin", title = "Two new {B}ayesian approximations of belief functions based on convex geometry", journal= "submitted to the IEEE Trans. on Systems, Man, and Cybernetics - part B", volume = "", issue = "", pages = "", year = "2006" } @article{Boucheron03, author = "S. Boucheron and E. Gassiat", title = "Optimal Error Exponents for {HMM} Order Estimation", journal= "IEEE Trans. Info. Th.", volume = "48", issue = "", pages = "964-980", year = "2003" } %% object tracking @article{Sidenbladh03, author = "H. Sidenbladh and M.J. Black", title = "Learning the Statistics of People in Images and Video", journal= "IJCV", volume = "54", issue = "", pages = "189-209", year = "2003" } @book{Blake98active, author = "A. Blake and M. Isard", title = "Active contours", publisher = "Springer-Verlag", address= "", year = "April 1998" } @inproceedings{Gennari02, author = "G. Gennari, A. Chiuso, F. Cuzzolin and R. Frezza", title = "Integrating Shape and Dynamic Probabilistic Models for Data Association and Tracking", booktitle= "CDC'02, Las Vegas, Nevada", editor = "", journal= "", volume = "", pages = "", year = "December 2002" } % reviews @inproceedings{Aggarwal94, author = "J. Aggarwal and Q. Cai and W. Liao and B. Sabata", title = "Articulated and Elastic Non-Rigid Motion: A Review", booktitle= "IEEE Proc. Nonrigid and Articulated Motion Workshop, Austin, Texas", editor = "", journal= "", volume = "", pages = "2-14", year = "1994" } @inproceedings{Aggarwal97, author = "J. Aggarwal and Q. Cai", title = "Human motion analysis: a review", booktitle= "IEEE Proc. Nonrigid and Articulated Motion Workshop", editor = "", journal= "", volume = "", pages = "90-102", year = "June 1997" } @article{Aggarwal98, author = "J. Aggarwal and Q. Cai and W. Liao and B. Sabata", title = "Nonrigid motion analysis: articulated and elastic motion", journal= "CVIU", volume = "70", issue = "2", pages = "142-156", year = "1998" } @article{Aggarwal99, author = "J. Aggarwal and Q. Cai", title = "Human motion analysis: a review", journal= "Computer Vision and Image Understanding", volume = "73", issue = "3", pages = "", year = "1999" } @article{Gavrila99, author = "D.M. Gavrila", title = "The visual analysis of human movement: a survey", journal= "Computer Vision and Image Understanding", volume = "73", issue = "1", pages = "82-98", year = "1999" } @article{Moeslund01, author = "T. Moeslund and E. Granum", title = "A Survey of Computer Vision-Based Human Motion Capture", journal= "Image and Vision Computing", volume = "81", pages = "231-268", year = "2001" } @techreport{Moeslund99a, author = "T. Moeslund", title = "Summaries of 107 Computer Vision-Based Human Motion Capture Papers", institution = "Laboratory of Image Analysis, Aalborg University, Denmark", year = "1999", } % fitting, modello cinematico @article{Orourke80, author = "J. O'Rourke and N. Badler", title = "Model-based analysis of human motion using constraint propagation", journal= "IEEE Trans. Pattern Analysis and Machine Intelligence", volume = "2", issue = "6", pages = "522-536", year = "1980" } % the estimated pose is projected onto a feasible manifold of realistic poses @inproceedings{Hunter97, author = "E.A. Hunter and P.H. Kelly and R.C. Jain", title = "Estimation of Articulated Motion Using Kinematically Constrained Mixture Densities", booktitle = "Workshop on Motion of Non-Rigid and Articulated Objects, Puerto Rico, USA", editor = "", journal= "", volume = "", pages = "", year = "1997" } % optical flow and articulated deformable model + Kalman @article{Pentland91, author = "A. Pentland and B. Horowitz", title = "Recovery of non-rigid motion and structure", journal= "IEEE Trans. Pattern Analysis and Machine Intelligence", volume = "13", issue = "7", pages = "730-742", year = "1991" } % parti deformabili @article{Pentland90, author = "A. Pentland", title = "Automatic Extraction of Deformable Models", journal= "Int. J. Computer Vision", volume = "4", issue = "", pages = "107-126", year = "1990" } % blob features @inproceedings{Azarbayejani96a, author = "A. Azarbayejani and A. Pentland", title = "Real-time self calibrating stereo person tracking using 3-D shape estimation from blob features", booktitle= "Proc. of the $13^{th}$ International Conference on Pattern Recognition", editor = "", journal= "", volume = "3", pages = "627-632", year = "1996" } @inproceedings{Azarbayejani96b, author = "A. Azarbayejani and C.R. Wren and A. Pentland", title = "Real-Time 3-D Tracking of the Human Body", booktitle= "IMAGE'COM 96, Bordeaux, France", editor = "", journal= "", volume = "", pages = "", year = "May 1996" } % Rehg e soci @techreport{Rehg93, author = "J. Rehg and T. Kanade", title = "Digiteyes: Vision-based human hand tracking", institution = "CS-TR-93-220, Carnegie Mellon University, School of Computer Science", year = "1993", } @inproceedings{Rehg94, author = "J. Rehg and T. Kanade", title = "Visual tracking of high dof articulated structures: an application to human hand tracking", booktitle= "Proc. of the Third European Conference on Computer Vision, Stockholm, Sweden", editor = "J. Eklundh", journal= "", volume = "2", pages = "35-46", year = "1994" } @inproceedings{Rehg95, author = "J. M. Rehg and T. Kanade", title = "Model-based tracking of self-occluding articulated objects", booktitle= "Proceedings of the International Conference on Computer Vision ICCV'95, Cambridge, MA", editor = "", journal= "", volume = "", pages = "618-623", year = "20-23 June 1995" } @PHDTHESIS{Rehg95a, author = "J. Rehg", title = "Visual analysis of high dof articulated objects with application to hand tracking", school = "Carnegie Mellon University", type = "{PhD} Dissertation", address = "", month = "April", year = "1995", note = "", } % introduzione dello Scaled Prismatic Model (2D) che non soffre di tutte le singolarità di un modello cinematico 3D @inproceedings{Morris98, author = "D. Morris and J.M. Rehg", title = "Singularity Analysis for Articulated Object Tracking", booktitle= "Proceedings of CVPR'98", editor = "", journal= "", volume = "", pages = "289-296", year = "1998" } % the prob. density of the state is a multimodal piecewise Gaussian % sampling, ipotesi multiple @inproceedings{Cham99, author = "T.-J. Cham and J. Rehg", title = "A multiple hypothesis approach to figure tracking", booktitle= "Proceedings of CVPR'99, Fort Collins, Colorado", editor = "", journal= "", volume = "2", pages = "239-245", year = "1999" } % problemi dei modelli cinematici nel caso monovista % vincoli addizionali per eliminare le ambiguità % metodo: ottimizzazione vincolata @inproceedings{DiFranco01, author = "D. DiFranco, T. Cham and J. Rehg", title = "Reconstruction of 3-D Figure Motion from 2D Correspondences", booktitle= "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition CVPR'01, Hawaii", editor = "", journal= "", volume = "", pages = "", year = "December 2001" } @inproceedings{Sminchisescu01, author = "C. Sminchisescu and B. Triggs", title = "Covariance Scaled Sampling for Monocular 3{D} Body Tracking", booktitle= "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition CVPR'01, Hawaii", editor = "", journal= "", volume = "", pages = "", year = "December 2001" } @techreport{Leventon98, author = "M.E. Leventon and W.T. Freeman", title = "Bayesian Estimation of 3{D} Human Motion from an Image Sequence", institution = "TR-98-06, Mitsubishi Electric Research Lab", year = "1998", } @inproceedings{Howe99, author = "N. Howe and M. Leventon and W. Freeman", title = "Bayesian Reconstruction of 3{D} Human Motion from Single-Camera Video", booktitle= "Neural Information Processing Systems, Denver, Colorado", editor = "", journal= "", volume = "", pages = "", year = "November 1999" } % metaxas e soci % quadrics and Lagrange equations @article{Terzopoulos91, author = "D. Terzopoulos and D. Metaxas", title = "Dynamic 3{D} Models with Local and Global Deformations: Deformable Superquadrics", journal= "IEEE Trans. Pattern Analysis and Machine Intelligence", volume = "13", issue = "7", pages = "703-714", year = "1991" } % parti deformabili @article{Metaxas93, author = "D. Metaxas and D. Terzopoulos", title = "Shape and Nonrigid Motion Estimation through Physics-Based Synthesis", journal= "IEEE Trans. Pattern Analysis and Machine Intelligence", volume = "15", issue = "6", pages = "580-591", year = "1993" } @inproceedings{Kakadiaris94, author = "I. A. Kakadiaris and D. Metaxas and R. Bajcsy", title = "Active part-decomposition, shape and motion estimations of articulated objects: A physics-based approach", booktitle= "Proceedings of the Conference on Computer Vision and Pattern Recognition CVPR'94", editor = "", journal= "", volume = "", pages = "980-984", year = "1994" } % edges, uso di forze su modelli fisici % selezione multivista per ogni parte del corpo % corrispondenza tra punti su contorni di occlusione e punti sul modello % forze applicate sul modello % Kalman predice futuro stato del modello per aiutare corrispondenze dei punti @inproceedings{Kakadiaris96, author = "I. A. Kakadiaris and D. Metaxas", title = "Model-based estimation of 3{D} human motion with occlusion based on active multi-viewpoint selection", booktitle= "Proceedings of the Conference on Computer Vision and Pattern Recognition CVPR'96, San Francisco, CA", editor = "", journal= "", volume = "", pages = "81-87", year = "18-20 June 1996" } % uso di forze su modelli fisici @article{Kakadiaris98, author = "I. A. Kakadiaris and D. Metaxas", title = "Three-Dimensional Human Body Model Acquisition from Multiple Views", journal= "International Journal on Computer Vision", volume = "30", issue = "3", pages = "191-218", year = "1998" } % Gavrila % edges @inproceedings{Gavrila95, author = "D. M. Gavrila and L. S. Davis", title = "Towards 3{D} Model-based tracking and recognition of human movement: A multi-view approach", booktitle= "International Workshop on Face and Gesture Recognition, Zurich", editor = "", journal= "", volume = "", pages = "", year = "1995" } @inproceedings{Gavrila96, author = "D. M. Gavrila and L. S. Davis", title = "3{D} Model-based Tracking of Humans in Action: A Multi-view Approach", booktitle= "Proceedings of CVPR'96, San Francisco, CA", editor = "", journal= "", volume = "", pages = "73-80", year = "18-20 June 1996" } % search and similarity measure between synthetized appearance and actual image % kinematic model @article{Hogg83, author = "D. Hogg", title = "Model-based vision: A program to see a walking person", journal= "Image Vision Comput.", volume = "1", issue = "1", pages = "5-20", year = "1983" } % fittano il modello sul gradiente delle immagini @inproceedings{Marchand99, author = "E. Marchand, P. Bouthemy, F. Chaumette and V. Moreau", title = "Robust real-time visual tracking using a 2{D}-3{D} model-based approach", booktitle= "Proceedings of ICCV'99, Kerkira, Greece", editor = "", journal= "", volume = "1", pages = "262-268", year = "September 1999" } @inproceedings{Cretual98, author = "A. Cretual and F. Chaumette and P. Bouthemy", title = "Complex Object Tracking by Visual Servoing Based on 2D Image Motion", booktitle = "International Conference on Pattern Recognition", editor = "", journal= "", volume = "", pages = "", year = "1998" } @inproceedings{Wang91, author = "J. Wang and G. Lorette and P. Bouthemy", title = "Analysis of Human Motion: A Model-Based Approach", booktitle = "Scandinavian Conference on Image Analysis", editor = "", journal= "", volume = "", pages = "", year = "1991" } @inproceedings{Wang92, author = "J. Wang and G. Lorette and P. Bouthemy", title = "Human Motion Analysis with Detection of Sub-Part Deformations", booktitle = "SPIE - Biomedical Image Processing and Three-Dimensional Microscopy", editor = "", journal= "", volume = "", pages = "", year = "1992" } % genetic algorithms @inproceedings{Ohya94, author = "J. Ohya and F. Kishino", title = "Human Posture Estimation from Multiple Images Using Genetic Algorithm", booktitle= "Proceedings of ICPR", editor = "", journal= "", volume = "", pages = "", year = "1994" } @inproceedings{Perales94, author = "F.J. Perales and J. Torres", title = "A system for human motion matching between synthetic and real images based on biomechanic graphical models", booktitle= "IEEE Workshop on Motion of Non-rigid and Articulated Objects, Austin, Texas", editor = "", journal= "", volume = "", pages = "", year = "1994" } % known motion patterns @inproceedings{Njastad99, author = "J. Njastad and S. Grinaker and G.A. Storhaug", title = "Estimating Parameters in a 2$\frac{1}{2}$D Human Model", booktitle = "$11^{th}$ Scandinavian Conference on Image Analysis, Greenland", editor = "", journal= "", volume = "", pages = "", year = "1999" } % edges, KF e modello del moto umano @article{Rohr94, author = "K. Rohr", title = "Towards Model-Based Recognition of Human Movements in Image Sequences", journal= "CVGIP: Image Understanding", volume = "59", issue = "", pages = "94-115", year = "1994" } % a gait parallel to the image plane is considered (known motion pattern) @book{Rohr97, author = "K. Rohr", title = "Human Movement Analysis Based on Explicit Motion Models, Chapter 8, pages 171-198", publisher = "Kluwer Academic Publisher", address= "Dordrecht Boston", year = "1997" } % map the training data into the phase space and use PCA to find a compact representation @inproceedings{Ong99, author = "E.J. Ong and S. Gong", title = "Tracking Hybrid 2{D}-3{D} Human Models from Multiple Views", booktitle = "International Workshop on Modeling People at ICCV'99, Corfu, Greece", editor = "", journal= "", volume = "", pages = "", year = "September 1999" } % learning all the likely trajectories in the state space from the training data @inproceedings{Pavlovic99, author = "V. Pavlovic and J. Rehg and T.-J. Cham and K. Murphy", title = "A Dynamic {B}ayesian Network Approach to Figure Tracking using Learned Dynamical Models", booktitle= "Proceedings of the ICCV'99", editor = "", journal= "", volume = "", pages = "94-101", year = "1999" } % alternative state space representation @inproceedings{Moeslund00, author = "T.B. Moeslund and E. Granum", title = "3{D} Human Pose Estimation using 2{D}-data and an Alternative Phase Space Representation", booktitle = "Workshop on Human Modeling, Analysis and Synthesis at CVPR2000, Hilton Head Island", editor = "", journal= "", volume = "", pages = "", year = "June 2000" } % phase space constraints @inproceedings{Campbell95, author = "L. Campbell and A. Bobick", title = "Recognition of Human Body Motion Using Phase Space Constraints", booktitle = "ICCV'95, Cambridge, MA", editor = "", journal= "", volume = "", pages = "", year = "1995" } % multiple cues @inproceedings{Moeslund00a, author = "T.B. Moeslund and E. Granum", title = "Multiple Cues in Model-Based Human Motion Capture", booktitle = "Fourth International Conference on Automatic Face and Gesture Recognition, Grenoble, France", editor = "", journal= "", volume = "", pages = "", year = "March 2000" } @article{Lien98, author = "C.-C. Lien and C.-L. Huang", title = "Model-Based Articulated Hand Motion Tracking for Gesture Recognition", journal= "Image and Vision Computing", volume = "16", pages = "121-134", year = "February 1998" } @inproceedings{Mikic01, author = "I. Mikic and M. Trivedi and E. Hunter and P. Cosman", title = "Articulated Body Posture Estimation from Multi-Camera Voxel Data", booktitle= "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition CVPR'01, Hawaii", editor = "", journal= "", volume = "", pages = "", year = "December 2001" } @PHDTHESIS{Mikic02, author = "I. Mikic", title = "Human Body Model Acquisition and Tracking using Multi-Camera Voxel Data", school = "University of California at San Diego", type = "{PhD} Dissertation", address = "", month = " ", year = "January 2002", note = "" } @inproceedings{Hunter97, author = "E. Hunter and P. Kelly and R. Jain", title = "Estimation of Articulated Motion using kinematically constrained mixture densities", booktitle= "IEEE Nonrigid and Articulated Motion Workshop, San Juan, Puerto Rico", editor = "", journal= "", volume = "", pages = "", year = "June 1997" } @PHDTHESIS{Hunter99, author = "E. Hunter", title = "Visual Estimation of Articulated Motion using the Expectation-Constrained Maximization Algorithm", school = "University of California at San Diego", type = "{PhD} Dissertation", address = "", month = " ", year = "October 1999", note = "" } %voxels @inproceedings{Cheung00, author = "G. Cheung and T. Kanade and J. Bouguet and M. Holler", title = "A Real Time System for Robust 3{D} Voxel Reconstruction of Human Motions", booktitle= "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition CVPR'00, Hilton Head Island, SC, USA", editor = "", journal= "", volume = "2", pages = "714-720", year = "July 2000" } @inproceedings{Covell00, author = "M. Covell and A. Rahimi and M. Harville and T. Darrell", title = "Articulated pose estimation using brightness- and depth-constancy constraints", booktitle= "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition CVPR'00, Hilton Head Island, SC, USA", editor = "", journal= "", volume = "", pages = "438-445", year = "July 2000" } % edges, particle filtering @inproceedings{Deutscher99, author = "J. Deutscher, B. North, B. Bascle and A. Blake ", title = "Tracking Through Singularities and Discontinuities by Random Sampling", booktitle= "Proceedings of ICCV'99", editor = "", journal= "", volume = "", pages = "1144-1149", year = "1999" } @inproceedings{Deutscher00, author = "J. Deutscher and A. Blake and I. Reid", title = "Articulated Body Motion Capture by Annealed Particle Filtering", booktitle= "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition CVPR'00, Hilton Head Island, SC, USA", editor = "", journal= "", volume = "", pages = "126-133", year = "July 2000" } @inproceedings{Deutscher01, author = "J. Deutscher and A. Davidson and I. Reid", title = "Automatic Partitioning of High Dimensional Search Spaces Associated with Articulated Body Motion Capture", booktitle = "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition CVPR'01, Hawaii", editor = "", journal= "", volume = "", pages = "", year = "December 2001" } % particle filtering: shape filter responses, Kalman @inproceedings{Moon01, author = "H. Moon, R. Chellappa and A. Rosenfeld", title = "3{D} object tracking using shape-encoded particle propagation", booktitle= "Proceeding of the Eighth IEEE International Conference on Computer Vision (ICCV'01), Vancouver, Canada", editor = "", journal= "", volume = "", pages = "307--314", year = "July 9-12, 2001" } % optical flow @techreport{Bregler97, author = "C. Bregler and J. Malik", title = "Video Motion Capture", institution = "UCB//CSD-97-973, Computer Science Dept., U.C. Berkeley", year = "1997", } % kinematic model, twists @inproceedings{Bregler98, author = "C. Bregler and J. Malik", title = "Tracking People with Twists and Exponential Maps", booktitle = "Proceedings of the Conference on Computer Vision and Pattern Recognition CVPR'98, Santa Barbara, CA", editor = "", journal= "", volume = "", pages = "", year = "June 1998" } % kinematic model @inproceedings{Bregler98a, author = "C. Bregler and J. Malik", title = "Estimating and Tracking Kinematic Chains", booktitle = "Proceedings of the Conference on Computer Vision and Pattern Recognition CVPR'98, Santa Barbara, CA", editor = "", journal= "", volume = "", pages = "", year = "June 1998" } % kinematic model + measured optical flow to update the model @inproceedings{Yamamoto91, author = "M. Yamamoto and K. Koshikawa", title = "Human motion analysis based on a robot arm model", booktitle = "CVPR'91", editor = "", journal= "", volume = "", pages = "664-665", year = "1991" } @inproceedings{Yamamoto98, author = "M. Yamamoto and A. Sato and S. Kawada and T. Kondo and Y. Osaki", title = "Incremental Tracking of Human Actions from Multiple Views", booktitle = "Proceedings of the Conference on Computer Vision and Pattern Recognition CVPR'98, Santa Barbara, CA", editor = "", journal= "", volume = "", pages = "2-7", year = "June 1998" } @inproceedings{Delamarre98, author = "Q. Delamarre and O. Faugeras", title = "Finding pose of hand in video images: a stereo-based approach", booktitle = "IEEE Proceedings of the International Conference on Automatic Face and Gesture Recognition FG'98, Japan", editor = "", journal= "", volume = "", pages = "585-590", year = "April 1998" } @inproceedings{Delamarre99, author = "Q. Delamarre and O. Faugeras", title = "3{D} Articulated Models and Multi-View Tracking with Silhouettes", booktitle = "Proceedings of ICCV'99, Kerkyra, Greece", editor = "", journal= "", volume = "2", pages = "716-721", year = "20-27 September 1999" } @article{Delamarre01, author = "Q. Delamarre and O. Faugeras", title = "3{D} Articulated Models and Multi-View Tracking with Physical Forces", journal= "Special Issue of Computer Vision and Image Understanding on Modeling People", volume = "81", issue = "3", pages = "328-357", year = "March 2001" } @article{Jung97, author = "S. Jung and K. Wohn", title = "Tracking and Motion Estimation of the Articulated Object: a Hierarchical Kalman Filter Approach", journal= "Real-Time Imaging", volume = "3", issue = "", pages = "415-432", year = "1997" } % disparity maps -> stereo data % EKF per imporre vincoli articolari % modello della profondità -> rete Bayesiana @inproceedings{Jojic99, author = "N. Jojic, M. Turk and T. Huang", title = "Tracking Self-Occluding Articulated Objects in Dense Disparity Maps", booktitle= "Proceedings of the IEEE International Conference on Computer Vision ICCV'99, Corfu, Greece", editor = "", journal= "", volume = "", pages = "", year = "September 1999" } @inproceedings{Jojic98, author = "N. Jojic and J. Gu and H.C. Shen and T. Huang", title = "3-D Reconstruction of Multipart Self-Occluding Objects", booktitle = "Asian Conference on Computer Vision", editor = "", journal= "", volume = "", pages = "", year = "1998" } % head tracking, no vincoli articolari % stereo data + altro @inproceedings{Darrell98, author = "T. Darrell, G. Gordon, M. Harville and J. Woodfill", title = "Integrated Person Tracking Using Stereo, Color, and Pattern Detection", booktitle= "CVPR'98", editor = "", journal= "", volume = "", pages = "601-608", year = "1998" } % stereo data from 3 cameras + ellipsoids to model the a human arm @inproceedings{Plankers99, author = "R. Plankers, P. Fua and N. D'Apuzzo", title = "Automated Body Modeling from Video Sequences", booktitle = "International Workshop on Modeling People at ICCV'99, Corfu, Greece", editor = "", journal= "", volume = "", pages = "", year = "September 1999" } @inproceedings{Fua98, author = "P. Fua and A. Gruen and R. Plankers and N. D'Apuzzo and D. Thalmann", title = "Human Body Modeling and Motion Analysis From Video Sequences", booktitle = "International Symposium on Real Time Imaging and Dynamic Analysis, Hakodate, Japan", editor = "", journal= "", volume = "", pages = "", year = "June 1998" } % volumetrico @inproceedings{Bottino98, author = "A. Bottino, A. Laurentini and P. Zuccone", title = "Towards Non-intrusive Motion Capture", booktitle = "Asian Conf. on Computer Vision", editor = "", journal= "", volume = "", pages = "", year = "1998" } @inproceedings{Yaniz98, author = "C. Yaniz, J. Rocha and F. Perales", title = "3{D} Region Graph for Reconstruction of Human Motion", booktitle = "Workshop on Perception of Human Motion at ECCV", editor = "", journal= "", volume = "", pages = "", year = "1998" } % parameterized (affine) optical flow estimation + robust regression scheme @inproceedings{Black95, author = "M.J. Black and Y. Yacoob", title = "Tracking and Recognizing Rigid and Non-rigid Facial Motions Using Local Parametric Models of Image Motions", booktitle= "Proceedings of the International Conference on Computer Vision ICCV'95, Cambridge, MA", editor = "", journal= "", volume = "", pages = "374-381", year = "1995" } % parameterized optical flow @inproceedings{Ju96, author = "S.X. Ju and M.J. Black and Y. Yacoob", title = "Cardboard People: A Parameterized Model of Articulated Motion", booktitle= "Proceedings of the International Conference on Automatic Face and Gesture Recognition", editor = "", journal= "", volume = "", pages = "38-44", year = "1996" } % flow @inproceedings{Yacoob98, author = "Y. Yacoob and L. Davis", title = "Learned temporal models of image motion", booktitle= "ICCV'98", editor = "", journal= "", volume = "", pages = "446-453", year = "1998" } % eigenspaces for tracking: parameterized optical flow estimation @inproceedings{Black96, author = "M.J. Black and A.D. Jepson", title = "EigenTracking: Robust Matching and Tracking of Articulated Objects Using a View-Based Representation", booktitle= "ECCV'96", editor = "", journal= "", volume = "", pages = "329-342", year = "1996" } % edges % quantitative test using a rectangular pattern on a table % predizione del modello @inproceedings{Goncalves95, author = "L. Goncalves, E. Di Bernardo, E. Ursella ad P. Perona", title = "Monocular Tracking of the Human Arm in 3{D}", booktitle= "Proceedings of the International Conference on Computer Vision ICCV'95, Cambridge, MA", editor = "", journal= "", volume = "", pages = "764-770", year = "1995" } % a texture model of each limb is generated offline + a commercial motion capture system is used to get ground truth + % they derive a mapping between each pixel and the position on the cylinder modeling the limb (building a texture model for each limb) + % models are represented by PCA as a linear space @inproceedings{Sidenbladh00, author = "H. Sidenbladh and F. de la Torre and M.J. Black", title = "A framework for modeling the appearance of 3{D} articulated figures", booktitle= "Int. Conference on Automatic Face and Gesture Recognition", editor = "", journal= "", volume = "", pages = "", year = "2000" } % stocastico, modello del moto @inproceedings{Sidenbladh00a, author = "H. Sidenbladh and M.J. Black and D.J. Fleet", title = "Stochastic Tracking of 3{D} Human Figures using 2D Image Motion", booktitle= "ECCV'00", editor = "", journal= "", volume = "", pages = "", year = "2000" } @inproceedings{Lowe90, author = "D. Lowe", title = "Integrated treatment of matching and measurement errors for robust model-based motion tracking", booktitle= "ICCV'90", editor = "", journal= "", volume = "", pages = "436-440", year = "1990" } % registration % model-based line tracking @article{Lowe90a, author = "D. Lowe", title = "Fitting parameterised 3-D models to images", journal= "IEEE Trans. PAMI", volume = "13", issue = "5", pages = "441-450", year = "1991" } @article{Lowe92, author = "D. Lowe", title = "Robust model-based motion tracking through the integration of search and estimation", journal= "International Journal on Computer Vision", volume = "8", issue = "2", pages = "113-122", year = "1992" } %edges @incollection{Harris92, author = "C.J. Harris", title = "Tracking with rigid models", booktitle= "Active Vision", editor = "A. Black and A. Yuille", pages = "", publisher= "MIT Press, Cambridge, MA", year = "1992" } %edges @article{Crowley92, author = "J. Crowley and P. Stelmaszyk and T. Skordas and P. Puget", title = "Measurement and Integration of 3{D} Structures by Tracking Edge Lines", journal= "Int. J. Computer Vision", volume = "8", issue = "1", pages = "29-52", year = "1992" } % fusion edges + optical flow @article{Wachter99, author = "S. Wachter and H.H. Nagel", title = "Tracking persons in monocular image sequences", journal= "CVIU", volume = "74", issue = "3", pages = "174-192", year = "1999" } % numerical method for the matching problem @inproceedings{Wachter97, author = "S. Wachter and H.H. Nagel", title = "Tracking persons in monocular image sequences", booktitle = "Workshop on Motion of Non-Rigid and Articulated Objects, Puerto Rico, USA", editor = "", journal= "", volume = "", pages = "", year = "1997" } % contours % confronto tra silhouette proiettata e misurata, tramite area difference. Un arto alla volta % ci sono altri due riferimenti nella review grande @inproceedings{Kameda93, author = "Y. Kameda and M. Minoh and K. Ikeda", title = "Three Dimensional Pose Estimation of an Articulated Object from its Silhouette Image", booktitle = "Asian Conference on Computer Vision", editor = "", journal= "", volume = "", pages = "", year = "1993" } % come sopra, con ingrandimento delle silhouette per ridurre l'errore + pesi positivi e negativi nella differenza @inproceedings{Hu00, author = "C. Hu, Q. Tu, Y. Li and S. Ma", title = "Extraction of Parametric Human Model for Posture Recognition Using Genetic Algorithm", booktitle = "Fourth International Conference on Automatic Face and Gesture Recognition, Grenoble, France", editor = "", journal= "", volume = "", pages = "", year = "March 2000" } @inproceedings{Boyer95, author = "E. Boyer, M.-O. Berger", title = "3{D} Surface Reconstruction Using Occluding Contours", booktitle= "CAIP'95, Prague, Czech Republic", editor = "", journal= "LNCS", volume = "970", pages = "", year = "September 1995" } % object part found by optical flow and represented by contours, finally compared with the projected ones from the model @inproceedings{Meyer97, author = "D. Meyer and J. Denzler and H. Niemann", title = "Model Based Extraction of Articulated Objects in Image Sequences", booktitle = "Fourth International Conference on Image Processing", editor = "", journal= "", volume = "", pages = "", year = "1997" } @article{Seales95, author = "W.B. Seales and O.D. Faugeras", title = "Building Three-Dimensional Object Models from Image Sequences", journal= "CVIU", volume = "61", issue = "3", pages = "308-324", year = "1995" } @article{Vaillant92, author = "R. Vaillant and O. Faugeras", title = "Using Extremal Boundaries for 3-D Object Modeling", journal= "IEEE Trans. PAMI", volume = "14", issue = "2", pages = "157-173", year = "February 1992" } @article{Zheng94, author = "J.Y. Zheng", title = "Acquiring 3-D Models from Sequences of Contours", journal= "IEEE Trans. PAMI", volume = "16", issue = "2", pages = "163-178", year = "1994" } @article{Szeliski94, author = "R. Szeliski and S.B. Kang", title = "Recovering 3{D} Shape and Motion from Image Streams Using Nonlinear Least Squares", journal= "J. Vis. Comm. Im. Repr.", volume = "5", issue = "1", pages = "10-28", year = "1994" } @PHDTHESIS{Zhao93, author = "J. Zhao", title = "Moving Posture Reconstruction from Perspective Projections of Jointed Figure Motion", school = "University of Pennsylvania", type = "{PhD} Dissertation", address = "", month = "", year = "1993", note = "", } % fitting splines to silhouette @inproceedings{Baumberg94, author = "A. Baumberg and D. Hogg", title = "Learning Flexible Models from Image Sequences", booktitle= "ECCV'94, Stockholm", editor = "J. Eklundh", journal= "LNCS", volume = "800", pages = "299-308", year = "1994" } % texture: pure image + correlation for texture comparison % several cameras @inproceedings{Lerasle97, author = "F. Lerasle and G. Rives and M. Dhome", title = "Human Body Limbs Tracking by Multi-ocular Vision", booktitle = "Scandinavian Conference on Image Analysis, Lappeenranta, Finland", editor = "", journal= "", volume = "", pages = "", year = "1997" } % texture: pure image @article{Lerasle99, author = "F. Lerasle and G. Rives and M. Dhome", title = "Tracking of Human Limbs by Multiocular Vision", journal= "CVIU", volume = "75", issue = "3", pages = "229-246", year = "September 1999" } % CAD models @inproceedings{Daucher93, author = "N. Daucher and M. Dhome and J. Lapreste and G. Rives", title = "Modeled object pose estimation and tracking by monocular vision", booktitle= "BMVC'93, Guildford, UK", editor = "", journal= "", volume = "", pages = "249-258", year = "September 1993" } @inproceedings{Kollnig95, author = "H. Kollnig and H.-H. Nagel", title = "3{D} pose estimation by fitting image gradients directly to polyhedral models", booktitle= "ICCV'95, Boston, MA", editor = "", journal= "", volume = "", pages = "569-574", year = "May 1995" } @inproceedings{Tonko97, author = "M. Tonko and K. Schafer and F. Heimes and H.-H. Nagel", title = "Towards visual servoed manipulation of car engine parts", booktitle= "Proceedings of the IEEE International Conference on Robotics and Automation ICRA'97, Albuquerque, NM", editor = "", journal= "", volume = "4", pages = "3166-3171", year = "April 1997" } @article{Fitzgibbon97, author = "A. Fitzgibbon and D. Eggert and R. Fisher", title = "High-Level CAD Model Acquisition from Range Images", journal= "Computer-Aided Design", volume = "29", issue = "4", pages = "321-330", year = "1997" } @article{Werghi99, author = "N. Werghi, R. Fisher, A. Ashbrook and C. Robertson", title = "Object Reconstruction by Incorporating Geometric Constraints in Reverse Engineering", journal= "Computer-Aided Design", volume = "31", issue = "6", pages = "363-399", year = "1999" } @inproceedings{Bowden98, author = "R. Bowden and T. Mitchell and M. Sarhadi", title = "Reconstructing 3{D} pose and motion from a single camera view", booktitle= "BMVC'98, Southampton, UK", editor = "", journal= "", volume = "", pages = "904-913", year = "1998" } @inproceedings{Armstrong95, author = "M. Armstrong and A. Zisserman", title = "Robust object tracking", booktitle= "Proc. ACCV'95, Singapore", editor = "", journal= "", volume = "1", pages = "58-62", year = "December 1995" } @inproceedings{Beardsley96, author = "P. Beardsley and P. Torr and A. Zisserman", title = "3{D} model acquisition from extended image sequences", booktitle= "Proc. of ECCV'96, Cambridge, UK", editor = "", journal= "", volume = "2", pages = "683-695", year = "April 1996" } % contours, model based, fitting @inproceedings{Drummond00, author = "T. Drummond and R. Cipolla", title = "Real-time tracking of multiple articulated structures in multiple views", booktitle= "ECCV'00, Dublin, Ireland", editor = "", journal= "", volume = "", pages = "", year = "2000" } @inproceedings{Drummond99, author = "T. Drummond and R. Cipolla", title = "Real-time tracking of complex structures with on-line camera calibration", booktitle= "Proc. of BMVC'99, Nottingham", editor = "", journal= "", volume = "", pages = "574-583", year = "1999" } % model building: wireframes come feature + KF + feedback tra il tracker 2D e il filtro che stima il 3D @inproceedings{Brown00, author = "M. Brown, T. Drummond and R. Cipolla", title = "3{D} Model Acquisition by Tracking 2{D} Wireframes", booktitle= "BMVC2000", editor = "", journal= "", volume = "", pages = "", year = "2000" } % kinematic model + markers + kalman for data association + particle filtering @inproceedings{Ringer00, author = "M. Ringer, J. Lasenby", title = "Modelling and tracking of articulated motion from multiple camera views", booktitle= "BMVC'2000", editor = "", journal= "", volume = "", pages = "172-181", year = "2000" } % contour tracking, hough transform @inproceedings{Wunsch97, author = "P. Wunsch and S. Winkler and G. Hirzinger", title = "Real-time pose estimation of 3{D} objects from camera images using neural networks", booktitle= "ICRA'97", editor = "", journal= "", volume = "3", pages = "3232-3237", year = "1997" } % roba in bibliografia, non classificata @article{Herda00, author = "L. Herda and P. Fua and R. Plankers and R. Boulic and D. Thalmann", title = "Skeleton-based motion capture for robust reconstruction of human motion", journal= "Computer Animation", volume = "", issue = "", pages = "", year = "May 2000" } @inproceedings{HaLeYo99, AUTHOR = "G. Hager and S-W. Lee and B-J. You", TITLE = "Model-based 3-D Object Tracking using Projective Invariance", YEAR = "1999", BOOKTITLE = "Proceedings of the International Conference on Robotics and Automation" } @article{Koller93, author = "D. Koller and H.-H. Nagel", title = "Model-based object tracking in monocular image sequences of road traffic scenes", journal= "Int. J. Computer Vision", volume = "10", issue = "3", pages = "257-281", year = "1993" } @article{Comaniciu03, author = "D. Comaniciu and V. Ramesh and P. Meer", title = "Kernel-based object tracking", journal= "IEEE Trans. PAMI", volume = "25", issue = "5", pages = "", year = "2003" } % KF @inproceedings{Yamamoto95, author = "S. Yamamoto and Y. Mae and Y. Shirai and J. Miura", title = "Realtime multiple object tracking based on optical flows", booktitle= "Proc. Robotics and Automation", editor = "", journal= "", volume = "3", pages = "2328-2333", year = "1995" } @inproceedings{Okada96, author = "R. Okada and Y. Shirai and J. Miura", title = "Object tracking based on optical flow and depth", booktitle= "Proc. of the Conference on Multisensor Fusion and Integration for Intelligent Systems", editor = "", journal= "", volume = "", pages = "565-571", year = "1996" } % dynamic layer representation, MAP @inproceedings{Tao00, author = "H. Tao and H.S. Sawhney and R. Kumar", title = "Dynamic Layer Representation with Applications to Tracking", booktitle= "CVPR'00", editor = "", journal= "", volume = "2", pages = "134-141", year = "2000" } @article{Tao01, author = "H. Tao, H.S. Sawhney and R. Kumar", title = "Object tracking with {B}ayesian estimation of dynamic layer representation", journal= "IEEE Transactions on PAMI", volume = "24", issue = "1", pages = "75-89", year = "January 2002" } @inproceedings{Vincze99, author = "M. Vincze and M. Ayromlou and W. Kubinger", title = "An integrating framework for robust real-time 3{D} object tracking", booktitle= "ICVS'99", editor = "", journal= "", volume = "", pages = "135-150", year = "1999" } @inproceedings{Worrall94, author = "A.D. Worrall and G.D. Sullivan and K.D. Baker", title = "Pose refinement of active models using forces in 3{D}", booktitle = "ECCV'94", editor = "J. Eklundh", journal= "", volume = "2", pages = "341-352", year = "May 1994" } @article{Stephens90, author = "R.S. Stephens", title = "Real-time 3{D} object tracking", journal= "Image and Vision Computing", volume = "8", issue = "1", pages = "91-96", year = "1990" } @incollection{Verghese90, author = "G. Verghese and K. Gale and C.R. Dyer", title = "Real-time, parallel motion tracking of three-dimensional objects from spatiotemporal image sequences", booktitle= "Parallel Algorithms for Machine Intelligence and Vision", editor = "Kumar et al.", pages = "", publisher= "Springer-Verlag", year = "1990" } % extended Kalman filter @article{Wu89, author = "J.J. Wu and R.E. Rink and T.M. Caelli and V.G. Gourishankar", title = "Recovery of the 3-D location and motion of a rigid object through camera image", journal= "Int. J. Computer Vision", volume = "2", issue = "4", pages = "373-394", year = "1989" } @inproceedings{Kuch, author = "J.J. Kuch and T. Huang", title = "Vision based hand modeling and tracking for virtual teleconferencing and telecollaboration", booktitle = "Proc. of the Fifth ICCV", editor = "", journal= "", volume = "", pages = "666-672", year = "" } @inproceedings{Qian92, author = "R. Qian and T. Huang", title = "Motion analysis of articulated objects with applications to human ambulatory patterns", booktitle = "DARPA'92", editor = "", journal= "", volume = "", pages = "549-553", year = "1992" } @article{Hel-Or96, author = "Y. Hel-Or and M. Werman", title = "Constraint fusion for recognition and localization of articulated objects", journal= "Int. J. Computer Vision", volume = "19", issue = "1", pages = "5-28", year = "1996" } % fusion! @article{Hel-Or95, author = "Y. Hel-Or, M. Werman", title = "Pose estimation by fusing noisy data of different dimensions", journal= "IEEE PAMI", volume = "17", issue = "", pages = "195-201", year = "1995" } % Dickinson % part-based object representation % usa aspetti o viste per modellare le singole parti invece di interi oggetti (modularità, database ridotti) @incollection{Dickinson, author = "S.J. Dickinson and D. Metaxas", title = "Integrating Qualitative and Quantitative Object Representations in the Recovery and Tracking of 3-D Shape", booktitle= "Computational and Psychophysical Mechanism of Visual Coding", editor = "L. Harris and M. Jenkin", pages = "", publisher= "Cambridge University Press, New York, NY", year = "" } % segmentazione a parti qualitativa + imposizione di modelli deformabili + uso di forze generate dalle immagini + % predizione di occlusioni con EKF (le eq. di lagrange delle forze sono il modello) @inproceedings{Chan94, author = "M. Chan and D. Metaxas and S. Dickinson", title = "A new approach to tracking 3-D objects in 2-D image sequences", booktitle = "Proc. of AAAI'94, Seattle, WA", editor = "", journal= "", volume = "", pages = "", year = "August 1994" } @article{Dickinson94, author = "S. Dickinson and D. Metaxas", title = "Integrating qualitative and quantitative shape recovery", journal= "Int. J. Computer Vision", volume = "13", issue = "3", pages = "1-20", year = "1994" } @article{Dickinson92, author = "S. Dickinson and A. Pentland and A. Rosenfeld", title = "3-D shape recovery using distributed aspect matching", journal= "IEEE Trans. PAMI", volume = "14", issue = "2", pages = "174-198", year = "1992" } % nonrigid motion @inproceedings{Huang90, author = "T.S. Huang", title = "Modeling, analysis and visualization on nonrigid object motion", booktitle = "Proc. of the $10^{th}$ IEEE Int. Conf. on Pattern Recognition", editor = "", journal= "", volume = "1", pages = "361-364", year = "1990" } @inproceedings{Duncan91, author = "J.S. Duncan and R.L. Owen and P. Anandan", title = "Measurement of Nonrigid Motion Using Contour Shape Descriptors", booktitle = "Proc. of CVPR'91", editor = "", journal= "", volume = "", pages = "318-324", year = "1991" } % stick figures % comparison of stick model with image silhouettes @article{Luo92, author = "Y. Luo and F.J. Perales and J.J. Villanueva", title = "An Automatic Rotoscopy System for Human Motion base on a Biomechanical Graphical Model", journal= "Computers and Graphics", volume = "16", issue = "4", pages = "", year = "1992" } % position of joints and segment length known @article{Lee85, author = "H.J. Lee and Z. Chen", title = "Determination of 3{D} Human Body Posture from a Single View", journal= "Computer Vision, Graphics, and Image Processing", volume = "30", issue = "", pages = "148-168", year = "1985" } % come sopra + modello del moto @article{Lee92, author = "H.J. Lee and Z. Chen", title = "Knowledge-Guided Visual Perception of 3-D Human Gait from a Single Image Sequence", journal= "IEEE Transactions on Systems, Man, and Cybernetics", volume = "22", issue = "2", pages = "", year = "March 1992" } % markers in 3D per i joints, e poi matching col modello 3D tramite grafi @inproceedings{Munkelt98, author = "O. Munkelt and C. Ridder and D. Hansel and W. Hafner", title = "A Model Driven 3{D} Image Interpretation System Applied to Person Detection in Video Images", booktitle = "International Conference on Pattern Recognition", editor = "", journal= "", volume = "", pages = "", year = "1998" } % the model stick figure is compared with a skeleton found from the silhouette % the problem is posed as an energy minimization one @article{Guo94, author = "Y. Guo, G. Xu and S. Tsuji", title = "Tracking Human Body Motion Based on a Stick Figure Model", journal= "Journal of Visual Communication and Image Representation", volume = "5", issue = "1", pages = "1-9", year = "1994" } @inproceedings{Fujiyoshi98, author = "H. Fujiyoshi and A.J. Lipton", title = "Real-Time Human Motion Analysis by Image Skeletonization", booktitle = "Workshop on Applications of Computer Vision", editor = "", journal= "", volume = "", pages = "", year = "1998" } % blobs % Wren e Pentland % 3D blobs of head and hands through "Pfinder" run on two camera views % + dynamical model + KF @techreport{Wren, author = "C.R. Wren and A.P. Pentland", title = "Dynaman: Recursive Modeling of Human Motion", institution = "TR-415, Medialab, MIT", year = "1997", } % behavior model @inproceedings{Wren98, author = "C.R. Wren and A.P. Pentland", title = "Dynamic Models of Human Motion", booktitle = "Int. Conf. on Automatic Face and Gesture Recognition, Nara, Japan", editor = "", journal= "", volume = "", pages = "", year = "1998" } % predizione del modello @inproceedings{Wren99, author = "C.R. Wren and A.P. Pentland", title = "Understanding Purposeful Human Motion", booktitle = "International Workshop on Modeling People at ICCV'99, Corfu, Greece", editor = "", journal= "", volume = "", pages = "", year = "September 1999" } % behavior model: six different motion models @inproceedings{Iwai99, author = "Y. Iwai and K. Ogaki and M. Yachida", title = "Posture Estimation Using Structure and Motion Models", booktitle = "ICCV'99, Corfu, Greece", editor = "", journal= "", volume = "", pages = "", year = "September 1999" } % simplified models @inproceedings{Cai96, author = "Q. Cai and J.K. Aggarwal", title = "Tracking Human Motion Using Multiple Cameras", booktitle = "International Conference on Pattern Recognition", editor = "", journal= "", volume = "", pages = "", year = "1996" } % aspect ratios between limbs of the body @inproceedings{Cai95, author = "Q. Cai and A. Mitiche and J.K. Aggarwal", title = "Tracking Human Motion in an Indoor Environment", booktitle = "International Conference on Image Processing", editor = "", journal= "", volume = "", pages = "", year = "1995" } @inproceedings{Bharatkumar94, author = "A.G. Bharatkumar and K.E. Diagle and M.G. Pandy and Q. Cai and J.K. Aggarwal", title = "Lower Limb Kinematics of Human Walking with the Medial Axis Transformation", booktitle = "Workshop on Motion of Non-Rigid and Articulated Objects, Austin, Texas", editor = "", journal= "", volume = "", pages = "", year = "1994" } % model from feature data % use 3D ground truth data for joints to train the system @inproceedings{Rosales00, author = "R. Rosales and S. Sclaroff", title = "Learning and Synthesizing Human Body Motion and Posture", booktitle = "Fourth Int. Conf. on Automatic Face and Gesture Recognition, Grenoble, France", editor = "", journal= "", volume = "", pages = "", year = "March 2000" } % path in the state space obtained from the training data are given to HMMs, whose states are linear path modeling by multivariate Gaussians @inproceedings{Brand99, author = "M. Brand", title = "Shadow Puppetry", booktitle = "ICCV'99, Corfu, Greece", editor = "", journal= "", volume = "", pages = "", year = "September 1999" } @article{Akita84, author = "K. Akita", title = "Image Sequence Analysis of Real World Human Motion", journal= "Pattern Recognition", volume = "17", issue = "1", pages = "73-83", year = "1984" } % key frames @inproceedings{Attwood89, author = "C.I. Attwood and G.D. Sullivan and K.D. Baker", title = "Model-based Recognition of Human Posture Using Single Synthetic Images", booktitle = "Fifth Alvey Vision Conference, Reading, UK", editor = "", journal= "", volume = "", pages = "", year = "1989" } @inproceedings{Yamamoto00, author = "M. Yamamoto and Y. Ohta and T. Yamagiwa and K. Yamanaka", title = "Human Action Tracking Guided by Key-Frames", booktitle = "Fourth Int. Conf. on Automatic Face and Gesture Recognition, Grenoble, France", editor = "", journal= "", volume = "", pages = "", year = "March 2000" } % others @inproceedings{Amat99, author = "J. Amat and M. Casals and M. Frigola", title = "Stereoscopic Systems for Human Body Tracking in Natural Scenes", booktitle = "Int. Workshop on Modeling People at ICCV'99", editor = "", journal= "", volume = "", pages = "", year = "September 1999" } @inproceedings{Hilton99, author = "A. Hilton", title = "Towards Model-Based Capture of a Person's Shape, Appearance and Motion", booktitle = "International Workshop on Modeling People at ICCV'99, Corfu, Greece", editor = "", journal= "", volume = "", pages = "", year = "September 1999" } % cue circles @inproceedings{Chung98, author = "J.M. Chung and N. Ohnishi", title = "Cue Circles: Image Feature for Measuring 3-D Motion of Articulated Objects Using Sequential Image Pair", booktitle = "Int. Conf. Automatic Face and Gesture Recognition, Nara, Japan", editor = "", journal= "", volume = "", pages = "", year = "1998" } @techreport{Christensen97, author = "C. Christensen and S. Corneliussen", title = "Tracking of Articulated Objects using Model-Based Computer Vision", institution = "Laboratory of Image Analysis, Aalborg University, Denmark", year = "1997", } @techreport{Corlin98, author = "C.R. Corlin and J. Ellesggard", title = "Real Time Tracking of a Human Arm", institution = "Laboratory of Image Analysis, Aalborg University, Denmark", year = "1998", } @inproceedings{Iwasawa99, author = "S. Iwasawa and J. Ohya and K. Takahashi and T. Sakaguchi and S. Kawato and K. Ebihara and S. Morishima", title = "Real-Time Estimation of Human Body Posture from Trinocular Images", booktitle = "International Workshop on Modeling People at ICCV'99, Corfu, Greece", editor = "", journal= "", volume = "", pages = "", year = "September 1999" } @article{Long91, author = "W. Long and Y.-H. Yang", title = "Log-Tracker: An Attribute Based Approach to Tracking Human Body Motion", journal= "Pattern Recognition and Artificial Intelligence", volume = "5", issue = "3", pages = "439-458", year = "1991" } @inproceedings{Niyogi94, author = "S.A. Niyogi and E.H. Adelson", title = "Analyzing and Recognizing Walking Figures in XYT", booktitle = "CVPR'94", editor = "", journal= "", volume = "", pages = "", year = "1994" } @inproceedings{Segawa99, author = "H. Segawa and T. Totsuka", title = "Torque-based Recursive Filtering Approach to the Recovery of 3{D} Articulated Motion from Image Sequences", booktitle = "ICCV'99, Corfu, Greece", editor = "", journal= "", volume = "", pages = "", year = "September 1999" } @inproceedings{Segawa00, author = "H. Segawa and H. Shioya and N. Hiraki and T. Totsuka", title = "Constraint-conscious Smoothing Framework for the Recovery of 3{D} Articulated Motion from Image Sequences", booktitle = "Fourth Int. Conf. on Automatic Face and Gesture Recognition, Grenoble, France", editor = "", journal= "", volume = "", pages = "", year = "March 2000" } @inproceedings{Zheng98, author = "J.Y. Zheng and S. Suezaki", title = "A Model Based Approach in Extracting and Generating Human Motion", booktitle = "International Conference on Pattern Recognition", editor = "", journal= "", volume = "", pages = "", year = "1998" } % generalized Hough tranform + probabilistic error model @inproceedings{Jurie97, author = "F. Jurie", title = "Model-based object tracking in cluttered scenes with occlusions", booktitle = "Intelligent Robots and Systems IROS'97", editor = "", journal= "", volume = "2", pages = "886-892", year = "1997" } % genetic algorithm, feature points @inproceedings{Kayanuma99, author = "M. Kayanuma and M. Hagiwara", title = "A new method to detect object and estimate the position and the orientation from an image using a 3-D model having feature points", booktitle = "IEEE Conference on Systems, Man and Cybernetics SMC'99", editor = "", journal= "", volume = "4", pages = "931-936", year = "1999" } @article{Linnainmaa88, author = "S. Linnainmaa and D. Harwood and L.S. Davis", title = "Pose Determination of a Three-Dimensional Object Using Triangle Pairs", journal= "IEEE Trans. PAMI", volume = "", issue = "", pages = "634-647", year = "September 1988" } @article{DeMenthon95, author = "D.F. DeMenthon and L.S. Davis", title = "Model-Based Object Pose in 25 Lines of Code", journal= "Int. J. Computer Vision", volume = "15", issue = "", pages = "123-141", year = "June 1995" } @inproceedings{David02, author = "P. David, D.F. DeMenthon and R. Duraiswami", title = "SoftPOSIT: Simultaneous Pose and Correspondence Determination", booktitle = "ECCV'02", editor = "A. Heyden et al.", journal= "LNCS 2352", volume = "", pages = "698-714", year = "2002" } @article{Lu00, author = "C.-P. Lu and G.D. Hager and E. Mjolsness", title = "Fast and Globally Convergent Pose Estimation from Video Images", journal= "IEEE Trans. PAMI", volume = "22", issue = "", pages = "610-622", year = "2000" } % copie cartacee da inserire A. Shahrokni and L. Vacchetti and V. Lepetit and P. Fua Automated Initialization of Polyhedral Object Tracking for Augmented Reality Applications Y. Sumi and Y. Kawai and T. Yoshimi and F. Tomita Recognition of 3D Free-Form Objects Using Segment-Based Stereo Vision K. Nirei and H. Saito and M. Mochimaru and S. Ozawa Human Hand Tracking from Binocular Image Sequences H. Moon and R. Chellappa and A. Rosenfeld Tracking of Human Activities Using Shape-encoded Particle Propagation E.-J. Ong and S. Gong A Dynamic Human Model using Hybrid 2D-3D Representations in Hierarchical PCA Space BMVC99 S.L. Dockstader and A. Murat Tekalp Tracking Multiple Objects in the Presence of Articulated and Occluded Motion % combina modello fisico e statistica di forme % fa uso di forze per deformare il modello % metodo semiautomatico T. Heap and D. Hogg 3D Deformable Hand Models % vedi sopra i contorni E. Boyer Object Models From Contour Sequences %% evidential reasoning @article{cuzzolin03proapprox, author = "F. Cuzzolin", title = "Probabilistic approximations of belief functions", journal= "preparing for submission to the IEEE Transactions on Systems, Man and Cybernetics B", volume = "", pages = "", year = "" } @article{cuzzolin02smc, author = "F. Cuzzolin", title = "Geometry of {D}empster's rule of combination", journal= "to appear on the IEEE Transactions on Systems, Man and Cybernetics B", volume = "", pages = "", year = "2003"} @article{cuzzolin03space, author = "F. Cuzzolin", title = "Geometrical structure of belief space and conditional subspaces", journal= "submitted to the IEEE Transactions on Systems, Man and Cybernetics C", volume = "", pages = "", year = "January 2003" } @article{cuzzolin02amai, author = "F. Cuzzolin", title = "Algebraic structure of the families of compatible frames of discernment", journal= "submitted to a Special Issue of the Annals of Mathematics and Artificial Intelligence", volume = "", pages = "", year = "September 2002" } @book{Aigner, author = "Martin Aigner", title = "Combinatorial Theory", publisher= "Classics in Mathematics, Springer", address= "New York", year = "1979" } @PHDTHESIS{cuzzolin01thesis, author = "F. Cuzzolin", title = "Visions of a generalized probability theory", school = "Universit\`a di Padova", type = "{PhD} Dissertation", address = "Dipartimento di Elettronica e Informatica", month = "19 February ", year = 2001, note = "", } @article{kyburg87bayesian, author = "H. Kyburg", title = "Bayesian and non-{B}ayesian evidential updating", journal= "Artificial Intelligence", volume = "31:3", pages = "271-294", year = "1987" } @inproceedings{Ha, author = "V. Ha and P. Haddawy", title = "Theoretical foundations for abstraction-based probabilistic planning", booktitle= "Proc. of the $12^{th}$ Conference on Uncertainty in Artificial Intelligence", editor = "", journal= "", volume = "", pages = "291-298", year = "August 1996" } % object detection @inproceedings{Perona1, author = "M. Weber and M. Welling and P. Perona", title = "Unsupervised learning of models for recognition", booktitle= "Proc. of the 6th European Conference on Computer Vision", editor = "", journal= "", volume = "1", pages = "18-32", year = "June/July 2000" } % KL distance @article{streit, author = "R. L. Streit", title = "The Moments of Matched and Mismatched Hidden Markov Models", journal = "IEEE Trans. on Acoustics, Speech, and Signal Processing", volume = "Vol. 38(4)", pages = "610-622", year = "April 1990" } @PhDTHESIS{karan, author = "M. Karan", title = "Frequency Tracking and Hidden Markov Models", text = "M. Karan, Frequency Tracking and Hidden Markov Models, PhD thesis, The Australian National University, March 1995", year = "1995" } @article{rabiner, author = "B. H. Juang and L. R. Rabiner", title = "A Probabilistic Distance Measure for Hidden Markov Models", journal = "AT\&T Technical Journal", volume = "Vol. 64(2)", pages = "391-408", year = "February 1985" } % other @inproceedings{black2, author = "M. J. Black", title = "Explaining optical flow events with parameterized spatio-temporal models", booktitle = "Proc. of Conference on Computer Vision and Pattern Recognition", editor = "", journal= "", volume = "1", pages = "326-332", year = "1999" } @inproceedings{black, author = "Y. Yacoob and M. J. Black", title = "Parameterized modeling and recognition of activities", booktitle = "Computer Vision and Image Understanding", editor = "", journal= "", volume = "73(2)", pages = "232-247", year = "1999" } @book{wertheimer, author = "M. Wertheimer", title = "Laws of organization in perceptual forms", publisher= "W. D. Ellis, editor, A Sourcebook of Gestalt Psychology, pages 331--363. Harcourt, Brace and Company", address= "", year = "1939" } @inproceedings{barronFB92, author = "J. L. Barron and D. J. Fleet and S. S. Beauchemin", title = "Performance of optical flow techniques", booktitle = "International Journal of Computer Vision", editor = "", journal= "", volume = "12(1)", pages = "43-77", year = "1994" } @inproceedings{PNF, author = "C. S. Pinhanez and A. F. Bobick", title = "Human action detection using PNF propagation of temporal constraints", booktitle = "Proc. of the Conference on Computer Vision and Pattern Recognition", editor = "", journal= "", volume = "", pages = "898-904", year = "1998" } @inproceedings{essa, author = "D. Moore and I. Essa and M. Hayes III", title = "Exploiting Human Actions and Object Context for Recognition Tasks", booktitle= "Proc. of the International Conference on Computer Vision", editor = "", journal= "", volume = "1", pages = "80-86", year = "1999" } @inproceedings{mada, author = "A. Madabhushi and J. K. Aggarwal", title = "A bayesian approach to human activity recognition", booktitle= "Proc. of the 2nd International Workshop on Visual Surveillance", editor = "", journal= "", volume = "", pages = "25-30", year = "June 1999" } @inproceedings{binder, author = "J. Binder and D. Koeller and S. Russell and K. Kanazawa", title = "Adaptive probabilistic networks with hidden variables", booktitle= "Machine Learning", editor = "", journal= "", volume = "29", pages = "213-244", year = "1997" } @inproceedings{brand, author = "M. Brand and N. Oliver and A. Pentland", title = "Coupled HMM for complex action recognition", booktitle = "Proc. of Conference on Computer Vision and Pattern Recognition", editor = "", journal= "", volume = "29", pages = "213-244", year = "1997" } @inproceedings{starner, author = "T. Starner and A. Pentland", title = "Real-time american sign language recognition from video using HMM", booktitle = "Proc. of ISCV 95", editor = "", journal= "", volume = "29", pages = "213-244", year = "1997" } @inproceedings{essaface, author = "I. A. Essa and A. O. Pentland", title = "Facial expression recognition using a dynamic model and motion energy", booktitle = "Proc. of the 5th Conference on Computer Vision", editor = "", journal= "", volume = "", pages = "360-367", year = "1995" } @inproceedings{blackface, author = "M. Black and P. Anandan", title = "The robust estimation of multiple motions: parametric and piecewise smooth flow fields", booktitle = "Computer Vision and Image Understanding", editor = "", journal= "", volume = "63(1)", pages = "75-104", year = "January 1996" } @inproceedings{donato, author = "G. Donato et al.", title = "Classifying facial actions", booktitle = "IEEE Journal on Pattern Analysis and Machine Intelligence", editor = "", journal= "", volume = "21(10)", pages = "974-989", year = "October 1999" } @inproceedings{gavrila, author = "D. M. Gavrila", title = "The visual analysis of human movement: A survey", booktitle = "Computer Vision and Image Understanding", editor = "", journal= "", volume = "73", pages = "82-98", year = "1999" } @inproceedings{ivanov, author = "Y. A. Ivanov and A. F. Bobick", title = "Recognition of visual activities and interactions by stochastic parsing", booktitle = "IEEE Trans. on Pattern Analysis and Machine Intelligence", editor = "", journal= "", volume = "22(8)", pages = "852-872", year = "2000" } @inproceedings{intille, author = "S. S. Intille and A. F. Bobick", title = "Visual recognition of multi agent action using binary temporal relations", booktitle = "Proc. of the Conf. on Computer Vision and Pattern Recognition", editor = "", journal= "", volume = "1", pages = "56-62", year = "1999" } @inproceedings{hoey, author = "J. Hoey and J. J. Little", title = "Representation and recognition of Complex Human Motion", booktitle = "Proc. of the Conference on Computer Vision and Pattern Recognition", editor = "", journal= "", volume = "1", pages = "752-759", year = "2000" } @inproceedings{perona, author = "M. Weber and M. Welling and P. Perona", title = "Unsupervised learning of models for recognition", booktitle= "Proc. of the 6th European Conference on Computer Vision", editor = "", journal= "", volume = "1", pages = "18-32", year = "June/July 2000" } @inproceedings{wu, author = "J. S. Liu and Y. Wu", title = "Parameter expansion for data augmentation", booktitle= "Journal of the American Statistical Association", editor = "", journal= "", volume = "94", pages = "1264-1274", year = "1999" } @inproceedings{poggio, author = "M. A. Giese and T. Poggio", title = "Morphable models for the analysis and synthesis of complex motion patterns", booktitle= "International Journal of Computer Vision", editor = "", journal= "", volume = "38(1)", pages = "1264-1274", year = "2000" } @inproceedings{bregler, author = "C. Bregler", title = "Learning and recognizing human dynamics in video sequences", booktitle= "Proc. of the Conference on Computer Vision and Pattern Recognition", editor = "", journal= "", volume = "", pages = "568-574", year = "1997" } @techreport{wilsononline, author = "A. D. Wilson and A. F. Bobick", title = "Realtime Online Adaptive Gesture Recognition", institution = "M.I.T. Media Laboratory, Tech. Rep. No. 505", year = "1999", } @inproceedings{wilsonparam, author = "A. D. Wilson and A. F. Bobick", title = "Parametric Hidden Markov Models for gesture recognition", booktitle = "IEEE Trans. on Pattern Analysis and Machine Intelligence", editor = "", journal= "", volume = "21(9)", pages = "884-900", year = "Sept. 1999" } %% works of mine @inproceedings{Cuzzolin97, author = "Andrea Sorrentino and Fabio Cuzzolin and Ruggero Frezza", title = "Using Hidden {M}arkov Models and Dynamic Size Functions for Gesture Recognition", booktitle= "Proceedings of the 8th British Machine Vision Conference (BMVC97)", editor = "Adrian F. Clark", journal= "", volume = "2", pages = "560-570", year = "September 1997" } @inproceedings{Cuzzolin99, author = "F. Cuzzolin and R. Frezza", title = "An Evidential Reasoning Framework for Object Tracking", booktitle= "SPIE - Photonics East 99", volume = "3840", pages = "13-24", year = "19-22 September 1999" } @inproceedings{Cuzzolin2000, author = "Fabio Cuzzolin and Ruggero Frezza", title = "Integrating feature spaces for object tracking", booktitle= "Proc. of MTNS2000", editor = "", journal= "", volume = "", pages = "", year = "21-25 June 2000" } @inproceedings{Cuzzolin2000d, author = "Fabio Cuzzolin", title = "Families of compatible frames of discernment as semimodular lattices", booktitle= "Proc. of the International Conference of the Royal Statistical Society (RSS2000)", editor = "", journal= "", volume = "", pages = "", year = "September 2000" } @inproceedings{Cuzzolin2000e, author = "Fabio Cuzzolin and Ruggero Frezza", title = "Sequences of belief functions and model-based data association", booktitle= "submitted to the IAPR Workshop on Machine Vision Applications (MVA2000)", editor = "", journal= "", volume = "", pages = "", year = "November 28-30, 2000" } @inproceedings{Cuzzolin2001, author = "Fabio Cuzzolin and Alessandro Bissacco and Ruggero Frezza and Stefano Soatto", title = "Towards Unsupervised Detection of Actions in Clutter", booktitle= "submitted to the International Conference on Computer Vision (ICCV2001)", editor = "", journal= "", volume = "", pages = "", year = "June 2001" } @inproceedings{cuzzolin01lattice, author = "Fabio Cuzzolin and Ruggero Frezza", title = "Lattice structure of the families of compatible frames", booktitle= "Proceedings of the $2^{nd}$ International Symposium on Imprecise Probabilities and their Applications (ISIPTA2001)", editor = "", journal= "", volume = "", pages = "", year = "26-29 June 2001" } @inproceedings{cuzzolin01space, author = "Fabio Cuzzolin and Ruggero Frezza", title = "Geometric analysis of belief space and conditional subspaces", booktitle= "Proceedings of the $2^{nd}$ International Symposium on Imprecise Probabilities and their Applications (ISIPTA2001)", editor = "", journal= "", volume = "", pages = "", year = "26-29 June 2001" } %% mathematical references @book{Farina, author = "Sergio Rinaldi and Lorenzo Farina", title = "I sistemi lineari positivi: teoria e applicazioni", publisher= "Citt\'a Studi Edizioni", address= "", year = "" } @book{Rosenbaum, author = "Albrecht Beutelspacher and Ute Rosenbaum", title = "Projective geometry", publisher= "Cambridge University Press", address= "Cambridge", year = "1998" } @book{Jacobson, author = "Nathan Jacobson", title = "Basic Algebra {I}", publisher= "Freeman and Company", address= "New York", year = "1985" } @book{Moore95, author = "R. Elliot, L. Aggoun and J. Moore", title = "Hidden {M}arkov models: estimation and control", publisher= "", address= "", year = "1995" } @book{Sikorski, author = "Roman Sikorski", title = "Boolean algebras", publisher= "Springer Verlag", address= "", year = "1964" } @book{Szasz, author = "Gabor Szasz", title = "Introduction to lattice theory", publisher= "Academic Press", address= "New York and London", year = "1963" } @book{Stern, author = "Manfred Stern", title = "Semimodular lattices", publisher= "Cambridge University Press", address= "", year = "1999" } @book{Rosenthal, author = "Kimmo I Rosenthal", title = "Quantales and their applications", publisher= "Longman scientific and technical", address= "Longman house, Burnt Mill, Harlow, Essex, UK", year = "1990" } @book{Novikov, author = "B.A. Dubrovin and S.P. Novikov and A.T. Fomenko", title = "Geometria Contemporanea 3", publisher= "Editori Riuniti", address= "", year = "1989" } @book{Novikov_russian, author = "B.A. Dubrovin and S.P. Novikov and A.T. Fomenko", title = "Sovremennaja geometrija. Metody i prilozenija", publisher= "Nauka", address= "Moscow", year = "1986" } @techreport{Socolovsky94, author = "H. Garcia-Compe\'an and J.M. L\'opez-Romero and M.A. Rodriguez-Segura and M. Socolovsky", title = "Principal bundles, connections and {BRST} cohomology", institution = "Los Alamos National Laboratory, hep-th/9408003", year = "July 1994", } %% object tracking and gesture recognition @techreport{Kanade93, author = "James M. Rehg and Takeo Kanade", title = "DigitEyes: Vision-Based Human Hand Tracking", institution = "School of Computer Science, Carnegie Mellon University, CMU-CS-93-220", year = "December 1993", } @techreport{Kanade94, author = "James M. Rehg and Takeo Kanade", title = "Visual Tracking of Self-Occluding Articulated Objects", institution = "School of Computer Science, Carnegie Mellon University, CMU-CS-94-224", year = "December 1994", } @inproceedings{Bobick95, author = "Aaron F. Bobick and Andrew D. Wilson", title = "Learning Visual Behavior for Gesture Analysis", booktitle= "IEEE Symposium on Computer Vision", editor = "", journal= "", volume = "", pages = "", year = "November 1995" } %% shape representation @inproceedings{Frosini91, author = "Patrizio Frosini", title = "Measuring Shape by Size Functions", booktitle = "Proceedings of SPIE on Intelligent Robots and Computer Vision X: Algorithms and Techniques, Boston, MA ", editor = "", journal= "", volume = "1607", pages = "122-133", year = "1991" } %% data association @book{Shalom88, author = "Yaakov Bar-Shalom and Thomas E. Fortmann", title = "Tracking and Data Association", publisher= "Academic Press, Inc.", address= "", year = "1988" } @inproceedings{Blake96, author = "Michael Isard and Andrew Blake", title = "Contour tracking by stochastic propagation of conditional density", booktitle= "Proceedings of the European Conference of Computer Vision (ECCV96)", editor = "", journal= "", volume = "", pages = "343-356", year = "1996" } @inproceedings{Bloem95, author = "Edwin A. Bloem and Henk A.P. Blom", title = "Joint probabilistic data association methods avoiding track coalescence", booktitle= "Proceedings of the 34th Conference on Decision and Control", editor = "", journal= "", volume = "", pages = "", year = "December 1995" } % other vision applications @article{Thrun, author = "Sebastian Thrun and Wolfgang Burgard and Dieter Fox", title = "A probabilistic approach to concurrent mapping and localization for mobile robots", journal= "Autonomous Robots", volume = "5", pages = "253-271", year = "1998" } @techreport{Rao, author = "Rajesh P.N. Rao and Dana H. Ballard", title = "Dynamic model of visual recognition predicts neaural response properties in the visual cortex", institution = "Department of computer science, University of Rochester", year = "November 1995", } %% classification @book{Duda, author = "Richard O. Duda and Peter E. Hart", title = "Pattern classification and scene analysis", publisher= "John Wiley and Sons Inc.", address= "", year = "1973" } %% Theory of evidence %% books @book{Shafer76, author = "G. Shafer", title = "A Mathematical Theory of Evidence", publisher= "Princeton University Press", address= "", year = "1976" } @book{goutsias97random, author = "John Goutsias and Ronald P.S. Mahler and Hung T. Nguyen", title = "Random sets: theory and applications ({IMA} {V}olumes in {M}athematics and {I}ts {A}pplications, {V}ol. 97)", publisher= "Springer-Verlag", address= "", year = "December 1997" } @book{matheronrandom, author = "G. Matheron", title = "Random Sets and Integral Geometry", publisher= "Wiley Series in Probability and Mathematical Statistics", address= "", year = "" } @book{definetti74, author = "B. De Finetti", title = "Theory of Probability", publisher= "Wiley, London", address= "", year = "1974" } @book{Grabish95, author = "Michel Grabisch and Hung T. Nguyen and Elbert A. Walker", title = "Fundamentals of uncertainty calculi with applications to fuzzy inference", publisher= "Kluwer Academic Publishers", address= "", year = "1995" } @book{Walley91, author = "Peter Walley", title = "Statistical Reasoning with Imprecise Probabilities", publisher= "Chapman and Hall", address= "London", year = "1991" } @BOOK{km95book, AUTHOR = {Jurg Kohlas and Paul-Andr\'e Monney}, TITLE = {A Mathematical Theory of Hints. An Approach to Dempster-Shafer Theory of Evidence}, PUBLISHER = {Springer-Verlag}, YEAR = {1995}, VOLUME = {425}, SERIES = {Lecture Notes in Economics and Mathematical Systems} } @BOOK{smithson1989, author = {M. J. Smithson}, title = {Ignorance and Uncertainty: Emerging Paradigms}, year = 1989, publisher = {Springer}, address = {New York (NY)} } @BOOK{goodman85uncertainty, author = {I. R. Goodman and Hung T. Nguyen}, title = {Uncertainty Models for Knowledge-based systems}, year = 1985, publisher = {North Holland}, address = {New York} } @BOOK{lee95fuzzy, author = {E. S. Lee and Q. Zhu}, title = {Fuzzy and Evidential Reasoning}, year = 1995, publisher = {Physica-Verlag}, address = {Heidelberg} } @BOOK{klir1988, author = {G. J. Klir and T. A. Folger}, title = {Fuzzy Sets, Uncertainty and Information}, year = 1988, publisher = {Prentice Hall}, address = {Englewood Cliffs (NJ)} } @BOOK{krause1993, author = {P. Krause and D. Clark}, title = {Representing Uncertain Knowledge}, year = 1993, publisher = {Kluwer}, address = {Dordrecht} } %% random sets and belief functions @ARTICLE{cooman1998a, author = {Gert {d}e Cooman and D. Aeyels}, title = {A random set description of a possibility measure and its natural extension}, year = {1998}, note = {submitted for publication} } @article{ross86random, author = "David Ross", title = "Random Sets Without Separability", journal= "Annals of Probability", volume = "14:3", pages = "1064-1069", year = "July 1986" } @article{Nguyen78, author = "H.T. Nguyen", title = "On Random Sets and Belief Functions", journal= "J. Mathematical Analysis and Applications", volume = "65", pages = "531-542", year = "1978" } @incollection{Nguyen97, author = "H.T. Nguyen and T. Wang", title = "Belief functions and random sets", booktitle= "Applications and Theory of Random Sets, The IMA Volumes in Mathematics and its Applications, Vol. 97", editor = "", pages = "243-255", publisher= "Springer", year = "1997" } @incollection{Hestir91, author = "H.T. Hestir and H.T. Nguyen and G.S. Rogers", title = "A random set formalism for evidential reasoning", booktitle= "Conditional Logic in Expert Systems", editor = "", pages = "309-344", publisher= "North Holland", year = "1991" } @techreport{Goutsias98, author = "John Goutsias", title = "Modeling random shapes: an introduction to random closed set theory", institution = "Department of Electrical and Computer Engineering, John Hopkins University, Baltimore, JHU/ECE 90-12", year = "April 1998", } %% fuzzy logic and belief functions @ARTICLE{dubois1987, author = {Didier Dubois and Henri Prade}, title = {The mean value of a fuzzy number}, year = 1987, journal = {Fuzzy Sets and Systems}, volume = 24, pages = { 279--300} } @article{kraetschmer98constraints, author = "Volker Kraetschmer", title = "Constraints on belief functions imposed by fuzzy random variables: Some technical remarks on Romer-Kandel", journal = "IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics", volume = "28", issue = "6", publisher = "IEEE", pages = "881-883", year = "1998", abstract="Roemer-Kandel investigated a new approach of fuzzy data analysis combining Dempster-Shafer theory and fuzzy set theory. Especially, belief measures are derived from fuzzy random variables but proved incompletely. This paper offers a completion using topological properties induced by the Hausdorff metric which is defined on the space of closed intervals of the real numbers. Moreover little corrections of some other assertions in the paper of Roemer-Kandel are presented. " } @article{heilpern97representation, author = "Stanislaw Heilpern", title = "Representation and application of fuzzy numbers", journal = "Fuzzy Sets and Systems", volume = "91", issue = "2", publisher = "Elsevier Science", pages = "259-268", year = "1997", abstract="In this paper we present the theoretical background of fuzzy numbers connected with the possibility and Dempster-Shafer theories. We describe some types of representation of fuzzy numbers and we study the notions of the distance and orders between fuzzy numbers based on these representations. The second part is devoted to the application of fuzzy numbers in data analysis, artificial intelligence and decision making." } @article{klir97constructing, author = "George J. Klir and Wang Zhenyuan and David Harmanec", title = "Constructing fuzzy measures in expert systems", journal = "Fuzzy Sets and Systems", volume = "92", issue = "2", publisher = "Elsevier Science", pages = "251-264", year = "1997", abstract="This paper is an overview of results regarding various representations of fuzzy measures and methods for constructing fuzzy measures in the context of expert systems, which were obtained by the authors and their associates during the last three years. Included are methods for constructing fuzzy measures by various transformations, by extension, by statistical inference, and by various data-driven methods based either on the Sugeno-integral or the Choquet-integral and using neural networks, genetic algorithms, or fuzzy relation equations." } @article{klir99fuzzy, author = "George J. Klir", title = "On fuzzy-set interpretation of possibility theory", journal = "Fuzzy Sets and Systems", volume = "108", issue = "3", publisher = "Elsevier Science", pages = "263-273", year = "1999", abstract="A revised fuzzy-set interpretation of possibility theory is introduced in this paper. Contrary to the standard fuzzy-set interpretation of possibility theory, which is coherent only for normal fuzzy sets, the revised interpretation is shown to be coherent for all fuzzy sets. It is also argued that the revised interpretation, which coincides with the standard one for normal fuzzy sets, is more meaningful on intuitive grounds. Prior to the introduction of the revised interpretation, previous efforts to overcome the well-known difficulties of the standard interpretation are critically examined, and it is demonstrated that none of them results in a coherent and meaningful interpretation of possibility theory." } @article{lucas99generalization, author = "Lucas Caro and Araabi Babak Nadjar", title = "Generalization of the Dempster-Shafer theory: a fuzzy-valued measure", journal = "IEEE Transactions on Fuzzy Systems", volume = "7", issue = "3", publisher = "IEEE", pages = "255-270", year = "1999", abstract="The Dempster-Shafer theory (DST) may be considered as a generalization of the probability theory, which assigns mass values to the subsets of the referential set and suggests an interval-valued probability measure. There have been several attempts for fuzzy generalization of the DST by assigning mass (probability) values to the fuzzy subsets of the referential set. The interval-valued probability measures thus obtained are not equivalent to the original fuzzy body of evidence. In this paper, a new generalization of the DST is put forward that gives a fuzzy-valued definition for the belief, plausibility, and probability functions over a finite referential set. These functions are all equivalent to one another and to the original fuzzy body of evidence. The advantage of the proposed model is shown in three application examples. It can be seen that the proposed generalization is capable of modeling the uncertainties in the real world and eliminate the need for extra preassumptions and preprocessing." } @article{yager96normalization, author = "Ronald R. Yager", title = "On the Normalization of Fuzzy Belief Structures", journal = "International Journal of Approximate Reasoning", volume = "14", issue = "2-3", publisher = "Elsevier Science", pages = "127-153", year = "1996", abstract="The issue of normalization in the fuzzy Dempster-Shafer theory of evidence is investigated. We suggest a normalization procedure called smooth normalization. It is shown that this procedure is a generalization of the usual Dempster normalization procedure. We also show that the usual process of normalizing an individual subnormal fuzzy subset by proportionally increasing the membership grades until the maximum membership grade is one is a special case of this smooth normalization process and in turn closely related to the Dempster normalization process. We look an alternative normalization process in the fuzzy Dempster-Shafer environment based on adding to the membership grade of subnormal focal elements the amount by which the fuzzy subset is subnormal." } @article{yen92computing, author = "John Yen", title = "Computing Generalized Belief Functions for Continuous Fuzzy Sets", journal = "International Journal of Approximate Reasoning", volume = "6", issue = "", publisher = "", pages = "1-31", year = "1992" } @article{young98updating, author = "Virginia R. Young and Shaun S. Wang", title = "Updating non-additive measures with fuzzy information", journal = "Fuzzy Sets and Systems", volume = "94", issue = "3", publisher = "Elsevier Science", pages = "355-366", year = "1998", abstract="We present several rules for updating non-additive set functions, defined and conditioned on fuzzy sets. Among these formulas are the Dempster-Shafer rule for belief functions and the Bayes conditioning rule. We develop the update formulas in the framework of non-additive measure and integration theory; thus, we generalize the work of Denneberg (1994). We explore the properties of the update rules and relate them to measures of (weak) fuzzy subsethood and to fuzzy inference operators. Specifically, we connect the Bayes update rule with Kosko\'s measure of fuzzy subsethood and with Mamdani\'s implication operator. Also, we connect the Dempster-Shafer update rule with the weak inclusion measure of fuzzy subsethood and with a well-known implication operator." } @article{yager99class, author = "Ronald R. Yager", title = "Class of fuzzy measures generated from a Dempster-Shafer belief structure", journal = "International Journal of Intelligent Systems", volume = "14", issue = "12", publisher = "John Wiley and Sons", pages = "1239-1247", year = "1999", abstract="Here the Dempster-Shafer belief structure is viewed as providing partial information about the underlying fuzzy measure associated with a uncertain variable. In this perspective there exists many possible fuzzy measures that can be associated with a Dempster-Shafer belief structure. Typically only two of these measures have been made explicit, those being the measure of belief and plausibility. Here we introduce a whole class of fuzzy measures that can be associated with a Dempster-Shafer belief structure. As an aid to choosing between these myriad of possibilities we discuss the entropy of a fuzzy measure. " } @article{mahler95combining, author = "Ronald P.S Mahler", title = "Combining ambiguous evidence with respect to ambiguous a priori knowledge. Part II: Fuzzy logic", journal = "Fuzzy Sets and Systems", volume = "75", issue = "3", publisher = "Elsevier Science", pages = "319-354", year = "1995", abstract="This paper describes fuzzy conditioned Dempster-Shafer (FCDS) theory, a probability-based calculus for dealing with possibly imprecise and vague evidence when the underlying a priori knowledge base is itself possibly imprecise and vague. FCDS has the same general form as existing fuzzy Dempster-Shafer theories. FCDS, however, employs a finite-level Zadeh fuzzy logic and a Dempster-Shafer-like combination operator which is conditioned to reflect the influence of any a priori knowledge base which can be modeled by a belief measure on finite-level fuzzy sets. We show that FCDS is grounded in probability theory-specifically, in the theory of random fuzzy sets. We also show that it is a generalization of Bayesian theory to the case when both evidence and a priori knowledge are imprecise and vague. We show that FCDS is consistent with the lattice structure of Zadeh\'s min-max fuzzy logic and that, in particular, it possesses an analog of the familiar Moebius transform." } @INCOLLECTION{feriet1982, author = {J. Kamp\'e de F\'eriet}, editor = {Gupta, M. M. and Sanchez, E.}, title = {Interpretation of membership functions of fuzzy sets in terms of plausibility and belief}, year = 1982, pages = {93--98}, booktitle = {Fuzzy Information and Decision Processes}, publisher = {North-Holland}, address = {Amsterdam} } @inproceedings{palacharla94understanding, author = "P. Palacharla and P.C. Nelson", title = "Understanding Relations between Fuzzy Logic and Evidential Reasoning Methods", booktitle= "Proceedings of Third IEEE International Conference on Fuzzy Systems", editor = "", journal= "", volume = "1", pages = "1933-1938", year = "1994" } @inproceedings{Renaud99, author = "Simon Petit-Renaud and Thierry Denoeux", title = " Handling different forms of uncertainty in regression analysis: a fuzzy belief structure approach", booktitle= "Proceedings of The Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty - Ecsqaru ( Lecture Notes in Computer Science Series)", editor = "", journal= "", volume = "", pages = "", year = "London, 5-9 July 1999" } %% neural networks and belief functions @article{wang98majority, author = "Chua-Chin Wang and Hon-Son Don", title = "The majority theorem of centralized multiple BAMs networks", journal = "Information Sciences", volume = "110", issue = "3-4", publisher = "Elsevier Science", pages = "179-193", year = "1998", abstract="A method for modeling the learning of belief combination in evidential reasoning using a neural network is presented. A centralized network composed of multiple bidirectional associative memories (BAMs) sharing a single output array of neurons is proposed to process the uncertainty management of many pieces of evidence simultaneously. The convergence properties of the multi-BAM network are proved. The combination process of evidence is considered as a resonant process through the multi-BAM networks. Most important of all, a majority rule of decision making in presentation of multiple evidence is also found by the study of signal-noise-ratio (SNR) of the multi-BAM network. Some simulation examples are given. The result is coherent with the intuition of reasoning." } %% hints and belief functions @book{Kohlas95, author = "Jurg Kohlas and Paul-Andr\'e Monney", title = "A Mathematical Theory of Hints - {A}n Approach to the {D}empster-{S}hafer Theory of Evidence", publisher= "Lecture Notes in Economics and Mathematical Systems, Springer-Verlag", address= "", year = "1995" } @ARTICLE{kohlas97allocation, AUTHOR = "Jurg Kohlas", TITLE = "Allocation of Arguments and Evidence Theory", JOURNAL = "Theoretical Computer Science", YEAR = "1997", VOLUME = "171", PAGES = "221-246", URL = "http://www2-iiuf.unifr.ch/tcs/publications/ps/kohlas97b.ps.Z", ABSTRACT = "The Dempster-Shafer theory of evidence is developed here in a very general setting. First, its symbolic or algebraic part is discussed as a body of arguments which contains an allocation of support and an allowment of possibility for each hypothesis. It is shown how such bodies of arguments arise in the theory of hints and in assumption-based reasoning in logic. A rule of combination of bodies of arguments is then defined which constitutes the symbolic counterpart of Dempster's rule. Bodies of evidence are next introduced by assigning probabilities to arguments. This leads to support and plausibility functions on some measurable hypotheses. As expected in Dempster-Shafer theory, they are shown to be set functions, monotone or alternating of infinite order respectively. It is shown how these support and plausibility functions can be extended to all hypotheses. This constitutes then the numerical part of evidence theory. Finally, combination of evidence based on the combination of bodies of arguments is discussed and a generalized version of Dempster's rule is derived. The approach to evidence theory proposed is general and is not limited to finite frames." } @incollection{kohlas95modelbased, AUTHOR = "Jurg Kohlas and Paul-Andr\'e Monney and R. Haenni and N. Lehmann", TITLE = "Model-Based Diagnostics Using Hints", BOOKTITLE = "Symbolic and Quantitative Approaches to Uncertainty, European Conference ECSQARU95, Fribourg", ORGANIZATION = "Lecture Notes in Computer Science, no. 946", PUBLISHER = "Springer", YEAR = "1995", EDITOR = "Ch. Fridevaux and J. Kohlas", PAGES = "259--266", URL = "http://www2-iiuf.unifr.ch/tcs/publications/ps/kmhl95.ps.Z", ABSTRACT = "It is often possible to describe the correct functioning of a system by a mathematical model. As long as observations or measurements correspond to the predictions made by the model, the system may be assumed to be functioning correctly. When, however, a discrepancy arises between the observations and the model-based predictions, then an explanation for this fact has to be found. The foundation of this approach to diagnostics has been laid by Reiter (1987). The explanations generated by his method, called diagnoses, are not unique in general. In addition, they are not weighed by a likelihood measure which would make it possible to compare them. We propose here the theory of hints -- an interpretation of the Dempster-Shafer Theory of Evidence -- as a very natural and general method for model-based diagnostics (for an introduction to the theory of hints, see Kohlas, Monney 1995). Note that Peng, Reggia (1990) and DeKleer, Williams (1987) also discuss probabilistic approaches to diagnostic problems." } @INCOLLECTION{kohlas95foundations, AUTHOR = {Jurg Kohlas}, TITLE = {Mathematical Foundations of Evidence Theory}, BOOKTITLE = {Mathematical Models for Handling Partial Knowledge in Artificial Intelligence}, ORGANIZATION = {}, PUBLISHER = {Plenum Press}, YEAR = {1995}, EDITOR = {G. Coletti and D. Dubois and R. Scozzafava}, PAGES = {31--64}, URL = {http://www2-iiuf.unifr.ch/tcs/publications/ps/kohlas95a.ps.Z} } @INPROCEEDINGS{kohlas94representation, AUTHOR = {Jurg Kohlas and Paul-Andr\'e Monney}, TITLE = {Representation of Evidence by Hints}, BOOKTITLE = {Advances in the Dempster-Shafer Theory of Evidence}, YEAR = {1994}, EDITOR = {R.R. Yager and J. Kacprzyk and M. Fedrizzi}, PUBLISHER = {John Wiley, New York}, PAGES = {473--492}, URL = {http://www2-iiuf.unifr.ch/tcs/publications/ps/km94c.ps.Z}, ABSTRACT = {This paper introduces a mathematical model of a hint as a body of imprecise and uncertain information. Hints are used to judge hypotheses: the degree to which a hint supports a hypothesis and the degree to which a hypothesis appears as plausible in the light of a hint are defined. This leads in turn to support- and plausibility functions. Those functions are characterized as set functions which are normalized and monotone or alternating of order $\infty$. This relates the present work to G. Shafer's mathematical theory of evidence. However, whereas Shafer starts out with an axiomatic definition of belief functions, the notion of a hint is considered here as the basic element of the theory. It is shown that a hint contains more information than is conveyed by its support function alone. Also hints allow for a straightforward and logical derivation of Dempster's rule for combining independent and dependent bodies of information. This paper presents the mathematical theory of evidence for general, infinite frames of discernment from the point of view of a theory of hints.} } @TECHREPORT{kohlas94mathematical, AUTHOR = {Jurg Kohlas}, TITLE = {Mathematical Foundations of Evidence Theory}, INSTITUTION = {Institute of Informatics, University of Fribourg}, YEAR = {1994}, TYPE = {}, NUMBER = {94-09}, ADDRESS = {}, MONTH = {}, NOTE = {Lectures to be presented at the International School of Mathematics ``G. Stampacchia" Mathematical Methods for Handling Partial Knowledge in Artificial Intelligence Erice, Sicily, June 19-25, 1994}, URL = {http://www2-iiuf.unifr.ch/tcs/publications/ps/kohlas94.ps.Z}, ABSTRACT = {} } @TECHREPORT{km90, AUTHOR = {Jurg Kohlas and Paul-Andr\'e Monney}, TITLE = {Modeling and Reasoning with Hints}, INSTITUTION = {Institute for Automation and Operations Research, University of Fribourg}, YEAR = {1990}, TYPE = {}, NUMBER = {174}, ADDRESS = {}, MONTH = {}, ABSTRACT = {Summary Paper of Theory of Hints. Introduction to math. DS-Theory. to what degree a body of information supports or contradicts, proves or disproves hypothesis. The math. model of Hints. Strike on the metro example. plausibility function. Basic probability assignments. Combining hints (DS-Rule). Difference between homogeneous/ heterogeneous and conflicting hints. Property of DS Rule. Conditioning Hints. Bayesian Hints. Frames of Discernment. Multivariate Models. Combining Hints on multivariate models. Conditional Information. Bayesian Modeling. Uncertain relations. Uncertain implication. Conditional probabilities. Link between DS-Rule and Bayes Formula. Introduction of qualitative Markov-Trees, Hypertrees. Belief updating. Arithmetic of numerical Hints. Appendix: Proofs.} } %% possibilities and belief functions @article{dubois01using, author = "Didier Dubois and M. Grabisch and Henri Prade and Philippe Smets", title = "Using the transferable belief model and a qualitative possibility theory approach on an illustrative example: the assessment of the value of a candidate", journal= "Intern. J. Intell. Systems", volume = "", pages = "", year = "2001" } @article{dubois97bayesian, author = "Didier Dubois and Henri Prade", title = "Bayesian conditioning in possibility theory", journal = "Fuzzy Sets and Systems", volume = "92", issue = "2", publisher = "Elsevier Science", pages = "223-240", year = "1997", abstract="In this paper, possibility measures are viewed as upper bounds of ill-known probabilities, since a possibility distribution is a faithful encoding of a set of lower bounds of probabilities bearing on a nested collection of subsets. Two kinds of conditioning can be envisaged in this framework, namely revision and focusing. On the one hand, revision by a sure event corresponds to adding an extra constraint enforcing that this event is impossible. On the other hand, focusing amounts to a sensitivity analysis on the conditioned probability measures (induced by the lower bound constraints). When focusing on a particular situation, the generic knowledge encoded by the probability bounds is applied to this situation, without aiming at modifying the generic knowledge. It contrasts with revision where the generic knowledge is modified by the new constraint. This paper proves that focusing applied to a possibility measure yields a possibility measure again, which means that the conditioning of a family of probabilities, induced by lower bounds bearing on probabilities of nested events, can be faithfully handled on the possibility representation itself. Relationships with similar results in the belief function setting are pointed out. Lastly the application of possibilistic focusing to exception-tolerant inference is suggested." } @incollection{Shafer87c, author = "Glenn Shafer", title = "Belief functions and possibility measures", booktitle= "Analysis of Fuzzy Information 1: Mathematics and logic", editor = "Bezdek", pages = "51-84", publisher= " CRC Press", year = "1987" } %% capacities and belief functions @ARTICLE{chateauneuf1989, author = {A. Chateauneuf and J. Y. Jaffray}, title = {Some characterizations of lower probabilities and other monotone capacities through the use of {M}\"obius inversion}, year = 1989, journal = {Mathematical Social Sciences}, volume = 17, pages = {263--283} } @article{hendon96product, author = "Ebbe Hendon and Hans Jorgen Jacobsen and Birgitte Sloth and Torben Tranaes", title = "The Product of Capacities and Belief Functions", journal= "Mathematical Social Sciences", volume = "32", pages = "95-108", year = "1996" } @article{denneberg00totally, author = "Dieter Denneberg", title = "Totally monotone core and products of monotone measures", journal = "International Journal of Approximate Reasoning", volume = "24", issue = "2-3", publisher = "Elsevier Science", pages = "273-281", year = "2000", abstract="Several approaches to the product of non-additive monotone measures (or capacities) are discussed and a new approach is proposed. It starts with the Moebius product [E. Hendon, H.J. Jacobsen, B. Sloth, T. Tranaes, The product of capacities and belief functions, Mathematical Social Sciences 32 (1996) 95-108] of totally monotone measures and extends it by means of a supremum to general monotone measures. The sup runs over sets of totally monotone measures. These sets are defined like the core of monotone measures (or cooperative games). The new product is compatible with the partial order for arbitrary monotone measures." } @article{wang97choquet, author = "Zhenyuan Wang and George J. Klir", title = "Choquet Integrals and Natural Extensions of Lower Probabilities", journal = "International Journal of Approximate Reasoning", volume = "16", issue = "2", publisher = "Elsevier Science", pages = "137-147", year = "1997", abstract="Both the Choquet integral with respect to monotone set functions and the natural extensions of lower probabilities are generalizations of the Lebesgue integral with respect to «sigma»-additive measures. The relation between these generalizations is investigated. We show that the Choquet integral with respect to a belief measure is always greater than or equal to the corresponding natural extension. Also, we compare some concepts introduced in the theory of imprecise probabilities with concepts established in fuzzy measure theory, capacity theory, and Dempster-Shafer theory." } %% incidences @article{bundy85incidence, author = "A. Bundy", title = "Incidence calculus: A mechanism for probability reasoning", journal = "Journal of automated reasoning", volume = "1", issue = "", publisher = "", pages = "263-283", year = "1985" } @article{liu98method, author = "W. Liu and D. McBryan and A. Bundy", title = "Method of assigning incidences", journal = "Applied Intelligence", volume = "9", issue = "2", publisher = "Kluwer Academic Publishers", pages = "139-161", year = "1998", abstract="Incidence calculus is a probabilistic logic in which incidences, standing for the situations in which formulae may be true, are assigned to some formulae, and probabilities are assigned to incidences. However, numerical values may be assigned to formulae directly without specifying the incidences. In this paper, we propose a method of discovering incidences under these circumstances which produces a unique output comparing with the large number of outputs from other approaches. Some theoretical aspects of this method are thoroughly studied and the completeness of the result generated from it is proved. The result can be used to calculate mass functions from belief functions in the Dempster-Shafer theory of evidence (DS theory) and define probability spaces from inner measures (or lower bounds) of probabilities on the relevant prepositional language set. " } %% fundaments @article{smets83information, author = "Philippe Smets", title = "Information Content of an Evidence", journal= "International Journal of Man Machine Studies", volume = "19", pages = "33-43", year = "1983" } @article{wilson92howmuch, author = "Nic Wilson", title = "How Much Do You Believe", journal = "International Journal of Approximate Reasoning", volume = "6", issue = "", publisher = "Elsevier Science", pages = "345-365", year = "1992" } @article{provan92validity, author = "Gregory Provan", title = "The Validity of Dempster-Shafer Belief Functions", journal = "International Journal of Approximate Reasoning", volume = "6", issue = "", publisher = "Elsevier Science", pages = "389-399", year = "1992" } @article{walley00towards, author = "Peter Walley", title = "Towards a unified theory of imprecise probability", journal = "International Journal of Approximate Reasoning", volume = "24", issue = "2-3", publisher = "Elsevier Science", pages = "125-148", year = "2000", abstract="Coherent upper and lower probabilities, Choquet capacities of order 2, belief functions and possibility measures are amongst the most popular mathematical models for uncertainty and partial ignorance. Examples are given to show that these models are not sufficiently general to represent some common types of uncertainty. In particular, they are not sufficiently informative about expectations and conditional probabilities. Coherent lower previsions and sets of probability measures are considerably more general, but they may not be sufficiently informative for some purposes. Two other models for uncertainty, which involve partial preference orderings and sets of desirable gambles, are discussed. These are more informative and more general than the previous models, and they may provide a suitable mathematical foundation for a unified theory of imprecise probability." } @article{smets97normative, author = "Philippe Smets", title = "The normative representation of quantified beliefs by belief functions", journal = "Artificial Intelligence", volume = "92", issue = "1-2", publisher = "Elsevier Science", pages = "229-242", year = "1997", abstract="The use of belief functions has recently been advocated as an alternative to the use of probability functions in order to represent quantified beliefs. Such a proposal lacked justification. We present a set of requirements that justify the use of belief functions. The assessment of the validity of these requirements provides a tool for assessing the relative value of normative models of subjective behaviors." } @article{joslyn98towards, author = "Cliff Joslyn and Luis Rocha", title = "Towards a formal taxonomy of hybrid uncertainty representations", journal = "Information Sciences", volume = "110", issue = "3-4", publisher = "Elsevier Science", pages = "255-277", year = "1998", abstract="In this paper we present some ideas about how to formally relate various uncertainty representations together in a taxonomic structure, capturing both syntactic and semantic generalization. Fuzziness and nonspecificity are presumed as primitive concepts of uncertainty, and transitive and intransitive methods operating with nonspecificity and fuzziness are introduced to generate a base class of hybrid uncertainty representational forms. Additive, maximal, and interval constraints then complete the characterization of the most important hybrid forms." } @article{Ruspini92, author = "E. H. Ruspini and J.D. Lowrance and T. M. Strat", title = "Understanding evidential reasoning", journal= "International Journal of Approximate Reasoning", volume = "6", pages = "401--424", year = "1992" } @ARTICLE{williams1978, author = {P. M. Williams}, title = {On a new theory of epistemic probability}, year = 1978, journal = {British Journal for the Philosophy of Science}, volume = 29, pages = {375--387} } @article{dempster82lindleys, author = "A.P. Dempster", title = "Lindley's Paradox: Comment", journal= "Journal of the American Statistical Association", volume = "77:378", pages = "339-341", year = "June 1982" } @article{Shafer81, author = "Glenn Shafer", title = "Constructive probability", journal= "Synthese", volume = "48", pages = "309-370", year = "1981" } @article{Shafer85b, author = "Glenn Shafer", title = "Conditional probability", journal= "International Statistical Review", volume = "53", pages = "261-277", year = "1985" } @article{Shafer87d, author = "Glenn Shafer", title = "Probability judgment in artificial intelligence and expert systems", journal= "Statistical Science", volume = "2", pages = "3-44", year = "1987" } @article{Shafer90, author = "Glenn Shafer", title = "Perspectives on the theory and practice of belief functions", journal= "International Journal of Approximate Reasoning", volume = "4", pages = "323-362", year = "1990" } @article{Klir90, author = "G. J. Klir and A. Ramer", title = "Uncertainty in the Dempster-Shafer theory: a critical re-examination", journal= "International Journal of General Systems", volume = "18", pages = "155-166", year = "1990" } @article{Pearl90, author = "Judea Pearl", title = "Reasoning with belief functions: an analysis of compatibility", journal= "International Journal of Approximate Reasoning", volume = "4", pages = "363-389", year = "1990" } @article{pearl86hierarchy, author = "Judea Pearl", title = "On Evidential Reasoning in a Hierarchy of Hypotheses (printed abstract)", journal= "Artificial Intelligence", volume = "28:1", pages = "9-15", year = "1986" } @article{Pearl92, author = "Judea Pearl", title = "Rejoinder to comments on `reasoning with belief functions: an analysis of compatibility'", journal= "International Journal of Approximate Reasoning", volume = "6", pages = "425-443", year = "1992" } @article{Shafer90a, author = "Glenn Shafer", title = "Perspectives on the theory and practice of belief functions", journal= "International Journal of Approximate Reasoning", volume = "4", pages = "323-36", year = "1990" } @article{Shafer92, author = "Glenn Shafer", title = "Rejoinders to comments on `perspectives on the theory and practice of belief functions'", journal= "International Journal of Approximate Reasoning", volume = "6", pages = "445-480", year = "1992" } @article{smets92resolving, author = "Philippe Smets", title = "Resolving misunderstandings about belief functions'", journal= "International Journal of Approximate Reasoning", volume = "6", pages = "321-34", year = "1992" } @article{Wasserman92, author = "L. A. Wasserman", title = "Comments on shafer's `perspectives on the theory and practice of belief functions`", journal= "International Journal of Approximate Reasoning", volume = "6", pages = "367-375", year = "1992" } @article{Dempster67, author = "A. P. Dempster", title = "Upper and lower probability inferences based on a sample from a finite univariate population", journal= "Biometrika", volume = "54", pages = "515-528", year = "1967" } @article{Walley82frequentist, author = "Peter Walley and T. L. Fine", title = "Towards a frequentist theory of upper and lower probability", journal= "The Annals of Statistics", volume = "10", pages = "741-761", year = "1982" } @article{halpern92twoviews, author = "J. Y. Halpern and R. Fagin", title = "Two views of belief: belief as generalized probability and belief as evidence", journal= "Artificial Intelligence", volume = "54", pages = "275-317", year = "1992", abstract="Belief functions are mathematical objects defined to satisfy three axioms that look somewhat similar to the Kolmogorov axioms defining probability functions. We argue that there are (at least) two useful and quite different ways of understanding belief functions. The first is as a generalized probability function (which technically corresponds to the inner measure induced by a probability function). The second is as a way of representing evidence. Evidence, in turn, can be understood as a mapping from probability functions to probability functions. It makes sense to think of updating a belief if we think of it as a generalized probability. On the other hand, it makes sense to combine two beliefs (using, say, Dempster's rule of combination) only if we think of the belief functions as representing evidence. Many previous papers have pointed out problems with the belief function approach; the claim of this paper is that these problems can be explained as a consequence of confounding these two views of belief functions." } @ARTICLE{suppes1977, author = "P. Suppes and M. Zanotti", title = "On using random relations to generate upper and lower probabilities", year = "1977", journal = "Synthese", volume = "36", pages = "427-440" } @article{Kyburg87, author = "H. E. Kyburg", title = "Bayesian and non-Bayesian evidential updatinge", journal= "Artificial Intelligence", volume = "31", pages = "271-293", year = "1987", abstract = "Four main results are arrived at in this paper. (1) Closed convex sets of classical probability functions provide a representation of belief that includes the representations provided by Shafer probability mass functions as a special case. (2) The impact of ``uncertain evidence'' can be (formally) represented by Dempster conditioning, in Shafer's framework. (3) The impact of ``uncertain evidence'' can be (formally) represented in the framework of convex sets of classical probabilities by classical conditionalization. (4) The probability intervals that result from Dempster-Shafer updating on uncertain evidence are included in (and may be properly included in) the intervals that result from Bayesian updating on uncertain evidence." } @article{blackmondlaskey89assumptions, author = "Kathryn Blackmond Laskey and Paul E. Lehner", title = "Assumptions, beliefs and probabilities", journal = "Artificial Intelligence", volume = "41", issue = "1", publisher = "Elsevier Science", pages = "65-77", year = "1989", abstract="A formal equivalence is demonstrated between Shafer-Dempster belief theory and assumption-based truth maintenance with a probability calculus on the assumptions. This equivalence means that any Shafer-Dempster inference network can be represented as a set of ATMS justifications with probabilities attached to assumptions. A proposition's belief is equal to the probability of its label conditioned on label consistency. An algorithm is given for computing these beliefs. When the ATMS is used to manage beliefs, non-independencies between nodes are automatically and correctly accounted for. The approach described here unifies symbolic and numeric approaches to uncertainty management, thus facilitating dynamic construction of quantitative belief arguments, explanation of beliefs, and resolution of conflicts." } @article{lee88comparison, author = "Chia-Hoang Lee", title = "A comparison of two evidential reasoning schemes", journal = "Artificial Intelligence", volume = "35", issue = "1", publisher = "Elsevier Science", pages = "127-134", year = "1988", abstract="Cordon and Shortliffe [2] advocate the use of Dempster-Shafer (D-S) theory in the evidence-gathering process. It is stated that they are unaware of any formal model which could allow inexact reasoning at whatever level of abstraction. Pearl [3] later shows how evidential reasoning can be conducted in the same hypothesis space using a Bayesian model. The purpose of this note is to examine the difference between these two schemes, and to point out certain inconsistencies of this Bayesian model with the motives behind the use of the D-S model." } @article{denoeux99reasoning, author = "Thierry Denoeux", title = "Reasoning with Imprecise Belief Structures", journal= "International Journal of Approximate Reasoning", volume = "20", pages = "79-111", year = "1999" } @INCOLLECTION{shafer1976a, author = {Glenn Shafer}, editor = {Harper, W. L. and Hooker, C. A.}, title = {A theory of statistical evidence}, year = 1976, volume = 2, pages = {365--436}, booktitle = {Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science}, publisher = {Reidel}, address = {Dordrecht}, note = {with discussion} } @INCOLLECTION{zadeh1986, author = {L. A. Zadeh}, editor = {Kanal, L. N. and Lemmer, J. F.}, title = {Is probability theory sufficient for dealing with uncertainty in {AI}: a negative view}, year = 1986, pages = {103--116}, booktitle = {Uncertainty in Artificial Intelligence}, publisher = {North-Holland}, volume = 2, address = {Amsterdam} } @incollection{Smets88, author = "Philippe Smets", title = "Belief functions", booktitle= "Non-Standard Logics for Automated Reasoning", editor = "Ph. Smets and A. Mamdani and D. Dubois and H. Prade", pages = "253-286", publisher= "Academic Press, London", year = "1988" } @incollection{Shafer85a, author = "Glenn Shafer", title = "Nonadditive probability", booktitle= "Encyclopedia of Statistical Sciences", editor = "Kotz and Johnson", pages = "6, 271-276", publisher= "Wiley", year = "1985" } @incollection{Levi83, author = "I. Levi", title = "Consonance, dissonance and evidentiary mechanism", booktitle= "Festschrift for Soren Hallden", editor = "", pages = "27-42", publisher= "Theoria", year = "1983" } @inproceedings{wakker99dempster, author = "Peter P. Wakker", title = "Dempster-Belief Functions Are Based on the Principle of Complete Ignorance", booktitle= "Proceedings of the 1st International Sysmposium on Imprecise Probabilites and Their Applications", editor = "", journal= "", volume = "", pages = "535-542", year = "Ghent, Belgium, 29 June - 2 July 1999" } @inproceedings{Smets97FAPR2, author = "Philippe Smets and Roger Cooke", title = "How to Derive Belief Functions Within Probabilistic Frameworks?", booktitle= "Proceedings of the International Joint Conference on Qualitative and Quantitative Practical Reasoning (ECSQARU / FAPR '97)", editor = "", journal= "", volume = "", pages = "", year = "Bad Honnef, Germany, 9-12 June 1997" } @inproceedings{Ruspini87, author = "E.H. Ruspini", title = "Epistemic logics, probability and the calculus of evidence", booktitle= "Proc. 10th Intl. Joint Conf. on AI (IJCAI-87)", editor = "", journal= "", volume = "", pages = "924-931", year = "1987" } @inproceedings{Fagin88, author = "R. Fagin and J.Y. Halpern", title = "Uncertainty, belief and probability", booktitle= "Proc. Intl. Joint Conf. in AI (IJCAI-89)", editor = "", journal= "", volume = "", pages = "1161-1167", year = "1988" } @inproceedings{Lowrance82, author = "John D. Lowrance and T. D. Garvey", title = "Evidential reasoning: A developing concept", booktitle= "Proceedings of the Internation Conference on Cybernetics and Society", editor = "Institute of Electrical and Electronical Engineers", journal= "", volume = "", pages = "6-9", year = "1982" } @inproceedings{benferhat95belief, author = "S. Benferhat and A. Saffiotti and Ph. Smets", title = "Belief functions and default reasoning", booktitle= "Procs. of the 11th Conf. on Uncertainty in AI. Montreal, Canada", editor = "", journal= "", volume = "", pages = "19-26", year = "1995" } @techreport{Walley91coherent, author = "Peter Walley", title = "Coherent lower (and upper) probabilities", institution = "University of Warwick, Coventry (U.K.), Statistics Research Report 22", year = "1981", } @techreport{kramosil97probabilistic, author = "Ivan Kramosil", title = "Probabilistic Analysis of Dempster-Shafer Theory. Part One", institution = "Academy of Science of the Czech Republic, Technical Report 716", year = "1997", } @techreport{kramosil98probabilistic, author = "Ivan Kramosil", title = "Probabilistic Analysis of Dempster-Shafer Theory. Part Two.", institution = "Academy of Science of the Czech Republic, Technical Report 749", year = "1998", } %% frameworks @article{an93relation, author = "Z. An and D. A. Bell and J. G. Hughes", title = "Relation-Based Evidential Reasoning", journal = "International Journal of Approximate Reasoning", volume = "8", issue = "", publisher = "", pages = "231-251", year = "1993" } @article{Kramosil96nonnumerical, author = "Ivan Kramosil", title = "Expert systems with non-numerical belief functions", journal = "Problems of control and information theory", volume = "16", issue = "1", publisher = "Elsevier Science", pages = "39-53", year = "1996" } @article{wierzchon97modified, author = "S.T. Wierzchon and M.A. Klopotek", title = "Modified component valuations in valuation based systems as a way to optimize query processing", journal = "Journal of Intelligent Information Systems", volume = "9", issue = "2", publisher = "Kluwer Academic Publishers", pages = "157-180", year = "1997", abstract="Valuation-Based System (VBS for short) can represent knowledge in different domains including probability theory, Dempster-Shafer theory and possibility theory. More recent studies show that the framework of VBS is also appropriate for representing and solving Bayesian decision problems and optimization problems. In this paper after introducing the valuation based system framework, we present Markov-like properties of VBS and a method for resolving queries to VBS. " } @article{andersen96linear, author = "K.A. Andersen and J.N. Hooker", title = "A linear programming framework for logics of uncertainty", journal = "Decision Support Systems", volume = "16", issue = "1", publisher = "Elsevier Science", pages = "39-53", year = "1996", abstract="Several logics for reasoning under uncertainty distribute ``probability mass'' over sets in some sense. These include probabilistic logic, Dempster-Shafer theory, other logics based on belief functions, and second-order probabilistic logic. We show that these logics are instances of a certain type of linear programming model, typically with exponentially many variables. We also show how a single linear programming package can implement these logics computationally if one ``plugs in'' a different column generation subroutine for each logic, although the practicality of this approach has been demonstrated so far only for probabilistic logic." } @article{ngwenyama98generating, author = "Ojelanki K. Ngwenyama and Noel Bryson", title = "Generating belief functions from qualitative preferences: An approach to eliciting expert judgments and deriving probability functions", journal = "Data and Knowledge Engineering", volume = "28", issue = "2", publisher = "Elsevier Science", pages = "145-159", year = "1998", abstract="It has long been recognized that the capability of using qualitative preferences to generate numeric judgments in expert systems and intelligent decision support systems (ES/IDSS) is essential. Although qualitative preferences and expressions facilitate communication and are useful for thinking about complex problems there is no simple and straightforward way to transform them for computer processing. Thus, the developer of the ES/IDSS must work with each expert to transform his/her vague and incomplete preferences into numeric estimates. This is a very difficult task and few techniques are available to assist developers with it. In this paper we present a qualitative discriminant process (QDP) for eliciting qualitative preferences from experts and generating appropriate numerical representations, as required by ES/IDSS, that utilize the Dempster-Shafer Theory. This approach provides a strategy for generating consistent numeric values for belief functions from qualitative preferences that can be used with the Dempster rules. We illustrate the approach with a case example." } @article{polkowski96mereology, author = "L. Polkowski and A. Skowron", title = "Rough Mereology: A New Paradigm for Approximate Reasoning", journal = "International Journal of Approximate Reasoning", volume = "15", issue = "4", publisher = "Elsevier Science", pages = "333-365", year = "1996", abstract="We are concerned with formal models of reasoning under uncertainty. Many approaches to this problem are known in the literature: Dempster-Shafer theory, bayesian-based reasoning, belief networks, fuzzy logics, etc. We propose rough mereology as a foundation for approximate reasoning about complex objects. Our notion of a complex object includes approximate proofs understood as schemes constructed to support our assertions about the world on the basis of our incomplete or uncertain knowledge." } @article{den99reasoning, author = "Thierry Denoeux", title = "Reasoning with imprecise belief structures", journal = "International Journal of Approximate Reasoning", volume = "20", issue = "1", publisher = "Elsevier Science", pages = "79-111", year = "1999", abstract="This paper extends the theory of belief functions by introducing new concepts and techniques, allowing to model the situation in which the beliefs held by a rational agent may only be expressed (or are only known) with some imprecision. Central to our approach is the concept of interval-valued belief structure (IBS), defined as a set of belief structures verifying certain constraints. Starting from this definition, many other concepts of Evidence Theory (including belief and plausibility functions, pignistic probabilities, combination rules and uncertainty measures) are generalized to cope with imprecision in the belief numbers attached to each hypothesis. An application of this new framework to the classification of patterns with partially known feature values is demonstrated." } @ARTICLE{bk95, AUTHOR = {P. Besnard and Jurg Kohlas}, TITLE = {Evidence Theory Based on General Consequence Relations}, JOURNAL = {Int. J. of Foundations of Computer Science}, YEAR = {1995}, VOLUME = {6}, NUMBER = {2}, PAGES = {119-135}, URL = {http://www2-iiuf.unifr.ch/tcs/publications/ps/bk95.ps.Z}, ABSTRACT = {The Dempster-Shafer theory of evidence can be conceived as a theory of probability of provability. In fact, it has been shown that evidence theory can be developed based on assumption based reasoning. Taking this approach, reasoning is modeled in this paper by a consequence relation in the sense of Tarski. It is shown that it is possible to construct evidence theory on top of the very general logics defined by these consequence relations. Support functions can be derived which are, as usual, set functions, monotone of infinite order. Furthermore, plausibility functions can also be defined. However, as negation is not generally defined in these general logics, the usual duality relations between support and plausibility functions of Dempster-Shafer theory do not hold in general. But this symmetry can be installed progressively by specializing to logics enjoying more and more ``structural properties''} } @article{yager99modeling, author = "Ronald R. Yager", title = "Modeling uncertainty using partial information", journal = "Information Sciences", volume = "121", issue = "3-4", publisher = "Elsevier Science", pages = "271-294", year = "1999", abstract="We are concerned here with the issue of representing the available information, which is often only partial, about the value of a variable. We consider the Dempster-Shafer belief structure and describe a number of different semantics that can be associated with it. Among these is a probabilistic interpretation in which some of the information is not available, we do not have all the distributions. This probabilistic interpretation leads us to consider a view involving selecting balls from an urn. Using this urn framework as a representation of our partial knowledge about the value of a variable leads to number of different uncertainty representations depending upon what information is assumed known." } @article{liu96theory, author = "Liping Liu", title = "A Theory of Gaussian Belief Functions", journal = "International Journal of Approximate Reasoning", volume = "14", issue = "2-3", publisher = "Elsevier Science", pages = "95-126", year = "1996", abstract="A Gaussian belief function can be intuitively described as a Gaussian distribution over a hyperplane, whose parallel subhyperplanes are the focal elements. This paper elaborates on the idea of Dempster and Shafer and formally represents a Gaussian belief function as a wide-sense inner product and a linear functional over a variable space, and as their duals over a hyperplane in a sample space. By adapting Dempster's rule to the continuous case, it derives a rule of combination and proves its equivalence to its geometric description by Dempster. It illustrates by examples how mixed knowledge involving linear equations, multivariate Gaussian distributions, and partial ignorance can be represented and combined as Gaussian belief functions." } @article{liu99local, author = "Liping Liu", title = "Local computation of Gaussian belief functions", journal = "International Journal of Approximate Reasoning", volume = "22", issue = "3", publisher = "Elsevier Science", pages = "217-248", year = "1999", abstract="Gaussian belief functions represent logical and probabilistic knowledge for mixed variables, some of which are deterministic, some vacuous, and some Gaussian. They include as special types linear equations, statistical observations, multivariate Gaussian distributions, and vacuous belief functions. The notion of Gaussian belief functions was proposed by A.P. Dempster (Normal belief functions and the Kalman filter, Technical report, Department of Statistics, Harvard University, Cambridge, MA, 1990.), formalized by G. Shafer (A note on Dempster's Gaussian belief functions, Technical report, School of Business, University of Kansas, Lawrence, KS, 1992.) and L. Liu (International Journal of Approximate Reasoning 14 (1996) 95-126.); (in: D. Fisher, Hans-J. Lenz (Eds.), Learning Models from Data: AI and Statistics V, Springer, New York, NY, 1996, pp. 79-88.) and successfully applied in combining independent statistical models in L. Liu (Model combination using Gaussian belief functions, Technical report, School of Business, University of Kansas, Lawrence, KS, 1995.). In this paper, we propose a join-tree computation scheme for expert systems using Gaussian belief functions. We first represent Dempster's rule of combination obtained in Liu (1996) alternatively in terms of matrix sweepings. We then show the operations of Gaussian belief functions follow the axioms of P.P. Shenoy and G. Shafer (in: R.D. Shachter, T.S. Levitt, L.N. Kanal, J.F. Lemmer (Eds.), Uncertainty in Artificial Intelligence, vol. 4, North-Holland, Amsterdam, 1990, pp. 169-198.) and justify the possibility of a join-tree computation scheme for Gaussian Belief functions. The result enriches the theory of local computation by extending its applicability to the combination of statistical models and the integration of knowledge bases. Examples are carried out to illustrate how combined inference can be made in accordance with multiple statistical models using graphically structured belief function models." } @article{snow98vulnerability, author = "Paul Snow", title = "The vulnerability of the transferable belief model to Dutch books", journal = "Artificial Intelligence", volume = "105", issue = "1-2", publisher = "Elsevier Science", pages = "345-354", year = "1998" } @article{smets94transferable, author = "Philippe Smets and Robert Kennes", title = "The transferable belief model ", journal = "Artificial Intelligence ", volume = "66", issue = "2", publisher = "Elsevier Science", pages = "191-234", year = "1994", abstract=" We describe the transferable belief model, a model for representing quantified beliefs based on belief functions. Beliefs can be held at two levels: (1) a credal level where beliefs are entertained and quantified by belief functions, (2) a pignistic level where beliefs can be used to make decisions and are quantified by probability functions. The relation between the belief function and the probability function when decisions must be made is derived and justified. Four paradigms are analyzed in order to compare Bayesian, upper and lower probability, and the transferable belief approaches." } @incollection{Lowrance90, author = "John D. Lowrance and T.D. Garvey and Thomas M. Strat", title = "A framework for evidential reasoning systems", booktitle= "Readings in uncertain reasoning", editor = "Shafer and Pearl", pages = "611-618", publisher= "Morgan Kaufman", year = "1990" } @incollection{Hsia89a, author = "Y. Hsia and Prakash P. Shenoy", title = "An evidential language for expert systems", booktitle= "Methodologies for Intelligent Systems", editor = "Ras Z.", pages = "9-16", publisher= "North Holland", year = "1989" } @incollection{Saffiotti91, author = "Alessandro Saffiotti", title = "A hybrid belief system for doubtful agents", booktitle= "Uncertatiny in Knowledge Bases, Lecture Notes in Computer Science 251", editor = "", pages = "393-402", publisher= "Springer-Verlag", year = "1991" } @incollection{smets91other, author = "Philippe Smets", title = "The transferable belief model and other interpretations of Dempster-Shafer's model", booktitle= "Uncertainty in Artificial Intelligence, volume 6", editor = "P.P. Bonissone and M. Henrion and L.N. Kanal and J.F. Lemmer", pages = "375-383", publisher= "North-Holland, Amsterdam", year = "1991" } @incollection{Smets91a, author = "Philippe Smets and Y. T. Hsia and Alessandro Saffiotti and R. Kennes and H. Xu and E. Emkehrer", title = "The Transferable Belief Model", booktitle= "Symbolic and Quantitative Approaches to Uncertainty", editor = "Kruse R. and Siegel P.", pages = "91-96", publisher= "Springer Verlag, Lecture Notes in Computer Science No. 458, Berlin", year = "1991" } @inproceedings{Saffiotti90, author = "Alessandro Saffiotti", title = "A hybrid framework for representing uncertain knowledge", booktitle= "Procs. of the 8th AAAI Conf. Boston, MA", editor = "", journal= "", volume = "", pages = "653-658", year = "1990" } @inproceedings{smets00fusion, author = "Philippe Smets", title = "Data Fusion in the Transferable Belief Model", booktitle= "Proc. 3rd Intern. Conf. Inforation Fusion", editor = "", journal= "", volume = "", pages = "21-33", year = "Paris, France 2000" } @inproceedings{Lowrance86, author = "J. D. Lowrance and T. D. Garvey and T. M. Strat", title = "A framework for evidential-reasoning systems", booktitle= "Proc. of the 5th National Conference on Artificial Intelligence", editor = "", journal= "", volume = "", pages = "896-903", year = "1986" } @inproceedings{Zarley88a, author = "D.K. Zarley and Y.T. Hsia and Glenn Shafer", title = "Evidential reasoning using {DELIEF}", booktitle= "Proc. Seventh National Conference on Artificial Intelligence", editor = "", journal= "", volume = "1", pages = "205-209", year = "1988" } @inproceedings{Laskey88, author = "K. Laskey and P.E. Lehner", title = "Belief manteinance: an integrated approach to uncertainty management", booktitle= "Proceeding of the Seventh National Conference on Artificial Intelligence (AAAI-88)", editor = "", journal= "", volume = "1", pages = "210-214", year = "1988" } @techreport{Zarley88b, author = "D.K. Zarley", title = "An evidential reasoning system", institution = "No.206, University of Kansas", year = 1988, } @techreport{Lowrance87, author = "John D. Lowrance", title = "Evidential Reasoning with Gister: A Manual", institution = "Artificial Intelligence Center, SRI International, 333 Ravenswood Avenue, Menlo Park, CA.", year = 1987, } @techreport{Lowrance94, author = "John D. Lowrance", title = "Evidential Reasoning with Gister-CL: A Manual", institution = "Artificial Intelligence Center, SRI International, 333 Ravenswood Avenue, Menlo Park, CA.", year = 1994, } @techreport{Hsia89b, author = "Y. Hsia and Prakash P. Shenoy", title = "MacEvidence: A visual evidential language for knowledge-based systems", institution = "No 211, School of Business, University of Kansas", year = 1989, } %% continuous TOE @article{shafer79allocations, author = "Glenn Shafer", title = "Allocations of Probability", journal= "Annals of Probability", volume = "7:5", pages = "827-839", year = "1979" } %% computational analysis and algorithms @article{kennes92computational, author = "R. Kennes", title = "Computational Aspects of the Moebius Transformation of Graphs", journal= "IEEE Transactions on Systems, Man, and Cybernetics", volume = "22", pages = "201-223", year = "1992" } @article{tessem93approximations, author = "B. Tessem", title = "Approximations for Efficient Computation in the Theory of Evidence", journal= "Artificial Intelligence", volume = "61:2", pages = "315-329", year = "1993" } @article{Shafer87a, author = "Glenn Shafer and R. Logan", title = "Implementing Dempster's rule for hierarchical evidence", journal= "Artificial Intelligence", volume = "33", pages = "271-298", year = "1987", abstract="This article gives an algorithm for the exact implementation of Dempster's rule in the case of hierarchical evidence. This algorithm is computationally efficient, and it makes the approximation suggested by Gordon and Shortliffe unnecessary. The algorithm itself is simple, but its derivation depends on a detailed understanding of the interaction of hierarchical evidence." } @article{Shenoy86, author = "Glenn Shafer and Prakash P. Shenoy", title = "Propagating belief functions using local computations", journal= "IEEE Expert", volume = "1", pages = "(3), 43-52", year = "1986" } @ARTICLE{km91, AUTHOR = {Jurg Kohlas and Paul-Andr\'e Monney}, TITLE = {Propagating Belief Functions Through Constraint Systems}, JOURNAL = {Int. J. Approximate Reasoning}, YEAR = {1991}, VOLUME = {5}, PAGES = {433-461}, ABSTRACT = {} } @ARTICLE{xu96reasoning, AUTHOR = {H. Xu and Philippe Smets}, TITLE = {Reasoning in Evidential Networks with Conditional Belief Functions}, JOURNAL = {International Journal of Approximate Reasoning}, YEAR = {1996}, VOLUME = {14}, PAGES = {155-185}, ABSTRACT = {In the existing evidential networks applicable to belief functions, the relations among the variables are always represented by joint belief functions on the product space of the variables involved. In this paper, we use conditional belief functions to represent such relations in the network and show some relations between these two kinds of representations. We also present a propagation algorithm for such networks. By analyzing the properties of some special networks with conditional belief functions, called networks with partial dependency, we show that the computation for reasoning can be simplified.} } @article{xu95computing, author = "H. Xu", title = "Computing Marginals from the Marginal Representation in Markov trees", journal= "Artificial Intelligence", volume = "74", pages = "177-189", year = "1995" } @ARTICLE{kohlas89b, AUTHOR = {Jurg Kohlas}, TITLE = {Modeling Uncertainty with Belief Functions in Numerical Models}, JOURNAL = {Europ. J. of Operational Research}, YEAR = {1989}, VOLUME = {40}, PAGES = {377--388}, ABSTRACT = {} } @incollection{Shenoy88, author = "Prakash P. Shenoy and K. Mellouli", title = "Propagation of belief functions: a distributed approach", booktitle= "Uncertainty in Artificial Intelligence 2", editor = "Lemmer and Kanal", pages = "325-336", publisher= " North Holland", year = "1988" } @incollection{Xu94, author = "H. Xu and R. Kennes", title = "Steps towards an Efficient Implementation of Dempster-Shafer Theory", booktitle= "Advances in the Dempster-Shafer Theory of Evidence", editor = "R.R. Yager and M. Fedrizzi and J. Kacprzyk", pages = "153-174", publisher= "John Wiley and Sons, Inc.", year = "1994" } @incollection{Xu93, author = "H. Xu", title = "An Efficient Tool for Reasoning with Belief Functions Uncertainty in Intelligent Systems", booktitle= "Advances in the Dempster-Shafer Theory of Evidence", editor = "Bouchon-Meunier B., Valverde L. and Yager R. R.", pages = "215-224", publisher= "North-Holland: Elsevier Science", year = "1993" } @incollection{Thoma91, author = "H. M. Thoma", title = "Belief Function Computations", booktitle= "Conditional Logic in Expert Systems", editor = "", pages = "269-308", publisher= "North Holland", year = "1991" } @incollection{Wilson, author = "Nic Wilson", title = "Chapter 10 : Belief Functions Algorithms", booktitle= "Algorithms for Uncertainty and Defeasible Reasoning", editor = "", pages = "", publisher= "", year = "" } @inproceedings{Barnett81, author = "J.A. Barnett", title = "Computational methods for a mathematical theory of evidence", booktitle= "Proc. of the 7th National Conference on Artificial Intelligence (AAAI-88)", editor = "", journal= "", volume = "", pages = "868-875", year = "1981" } @inproceedings{Xu94a, author = "H. Xu", title = "Computing Marginals from the Marginal Representation in Markov Trees", booktitle= "Proc. of the 5th International Conference on Information Proceeding and Management of Uncertainty in Knowledge-Based Systems", editor = "", journal= "", volume = "", pages = "275-280", year = "1994" } @inproceedings{Xu92, author = "H. Xu", title = "An Efficient Tool for Reasoning with Belief Functions", booktitle= "Proc. of the 4th International Conference on Information Proceeding and Management of Uncertainty in Knowledge-Based Systems", editor = "", journal= "", volume = "", pages = "65-68", year = "1992" } @inproceedings{Xu91, author = "H. Xu", title = "An Efficient Implementation of the Belief Function Propagation", booktitle= "Proc. of the 7th Uncertainty in Artificial Intelligence", editor = "D\'{A}mbrosio B. D., Smets Ph. and Bonissone P. P.", journal= "", volume = "", pages = "425-432", year = "1991" } @inproceedings{Lehmann99, author = "Norbert Lehmann and Rolf Haenni", title = "An alternative to outward propagation for Dempster-Shafer Belief functions", booktitle= "Proceedings of The Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty - Ecsqaru ( Lecture Notes in Computer Science Series)", editor = "", journal= "", volume = "", pages = "", year = "London, 5-9 July 1999" } @INPROCEEDINGS{bissig97fastdivision, AUTHOR = {R. Bissig and Jurg Kohlas and N. Lehmann}, TITLE = {Fast-division architecture for Dempster-Shafer belief functions}, BOOKTITLE = {Qualitative and Quantitative Practical Reasoning, First International Joint Conference on Qualitative and Quantitative Practical Reasoning; ECSQARU--FAPR'97 }, YEAR = {1997}, EDITOR = {D. Gabbay and R. Kruse and A. Nonnengart and H.J. Ohlbach}, PAGES = {}, PUBLISHER = {Springer}, BOOKTITEL = {Lecture Notes in Artif. Intell.}, NOTE = {}, URL = {http://www2-iiuf.unifr.ch/tcs/publications/ps/bkl97.ps.Z} } %% theoretical advances @PHDTHESIS{Kong86a, author = "Augustine Kong", title = "Multivariate belief functions and graphical models", school = "Harvard University", type = "{PhD} Dissertation", address = "Department of Statistics", month = "", year = 1986, note = "", } @PHDTHESIS{Mellouli86, author = "K. Mellouli", title = "On the propagation of beliefs in networks using the Dempster-Shafer theory of evidence", school = "University of Kansas", type = "{PhD} Dissertation", address = "School of Business", month = "", year = 1986, note = "", } @article{krantz83priors, author = "David H. Krantz and John Miyamoto", title = "Priors and Likelihood Ratios as Evidence", journal = "Journal of the American Statistical Association", volume = " 78", issue = "382", publisher = "", pages = "418-423", year = "June 1983" } @article{yu94conditional, author = "Chunhai Yu and Fahard Arasta", title = "On Conditional Belief Functions", journal = "International Journal of Approxiomate Reasoning", volume = "10", issue = "", publisher = "Elsevier Science", pages = "155-172", year = "1994" } @article{Hajek96, author = "P. Hajek", title = "Getting Belief Functions from Kripke Models", journal = "International Journal of General Systems", volume = " 24", issue = "3", publisher = "", pages = "325-327", year = "1996" } @article{Kramosil95, author = "Ivan Kramosil", title = "Approximations of Believeability Functions under Incomplete Identification of Sets of Compatible States", journal = "Kybernetika", volume = "31", issue = "5", publisher = "", pages = "425-450", year = "1995" } @article{Kramosil96a, author = "Ivan Kramosil", title = "Dempster-Shafer Theory with Indiscernible States and Observations", journal = "International Journal of General Systems", volume = "25", issue = "2", publisher = "", pages = "147-152", year = "1996" } @article{Kramosil88, author = "Ivan Kramosil", title = "Expert Systems with Non-Numerical Belief Functions", journal = "Problems of Control and Information Theory", volume = "17", issue = "5", publisher = "", pages = "285-295", year = "1988" } @article{bryson98qualitative, author = "Noel Bryson and Ayodele Mobolurin", title = "Qualitative discriminant approach for generating quantitative belief functions", journal = "IEEE Transactions on Knowledge and Data Engineering", volume = "10", issue = "2", publisher = "IEEE", pages = "345-348", year = "1998", abstract="We present an approach that will be useful in knowledge acquisition from experts on the degree of belief in, or the probability of, the truthfulness of various propositions. Its advantages include exploring the given problem situation using linguistic quantifiers; avoiding the premature use of numeric measures; and identifying input data that is inconsistent with the theory of belief functions. " } @article{chateauneuf00ambiguity, author = "A. Chateauneuf and J.-C. Vergnaud", title = "Ambiguity reduction through new statistical data", journal = "International Journal of Approximate Reasoning", volume = "24", issue = "2-3", publisher = "Elsevier Science", pages = "283-299", year = "2000", abstract="We provide some objective foundations for a belief revision process in a situation where (i) the decision-maker's initial probabilistic knowledge is imprecise and characterized by the core of a belief function, (ii) expected new data are themselves consistent with a belief function with known focal sets and (iii) the revision process is based on belief function combination. We study the properties of the information value for such a revising in the Gilboa-Schmeidler multi-prior model." } @article{Wasserman90prior, author = "L.A. Wasserman", title = "Prior envelopes based on belief functions", journal = "Annals of Statistics", volume = "18", issue = "1", publisher = "", pages = "454-464", year = "1990" } @article{dubois90, author = "D. Dubois and H. Prade", title = "Consonant approximations of belief functions", journal = "International Journal of Approximate Reasoning", volume = "4", issue = "", publisher = "", pages = "419-449", year = "1990" } @article{kramosil97belief, author = "Ivan Kramosil", title = "Belief functions generated by signed measures", journal = "Fuzzy Sets and Systems", volume = "92", issue = "2", publisher = "Elsevier Science", pages = "157-166", year = "1997", abstract="It is a well-known fact that the usual and already classical combinatorial definition of belief function over (the power-set of) a f