Algebraic structure of the families of compatible frames of discernment


Fabio Cuzzolin 
Annals of Mathematics and Artificial Intelligence, 2005 

Abstract 
One of the major ideas of Shafer's mathematical theory of evidence is the introduction of uncertainty descriptions on
different representation domains of phenomena, called families of compatible frames of discernment. Here we are
going to analyze these families of frames from an algebraic point of view, studying the properties of minimal
refinements of collections of domains and introducing the internal operation of maximal coarsening to establish
the structure of semimodular lattice. Motivated by the search for a solution of the conflict problem
that arises from sensor fusion applications, we will show the connection between classical independence of
frames as Boolean subalgebras and independence of frames as elements of a locally finite Birkhoff lattice. This will
eventually suggest an algebraic solution of the conflict problem. 
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BibTeX Entry 
@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",
PAGES = "241274",
YEAR = "2005"
} 
