A geometric approach to the theory of evidence


Fabio Cuzzolin 
IEEE Transactions on Systems, Man, and Cybernetics  part C, 2008 

Abstract 
In this paper we propose a geometric approach to the theory of evidence based on convex geometric interpretations of
its two key notions of belief function and Dempster's sum. On one side, we analyze the geometry of belief functions as
points of a polytope in the Cartesian space called belief space, and discuss the intimate relationship between basic
probability assignment and convex combination. On the other side, we study the global geometry of Dempster's rule by
describing its action on those convex combinations. By proving that Dempster's sum and convex closure commute we become
able to depict the geometric structure of conditional subspaces, i.e. sets of belief functions conditioned by a given
function b. Natural applications of these geometric methods to classical problems like probabilistic approximation
and canonical decomposition are outlined. 
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BibTeX Entry 
@article{cuzzolin08smcc,
AUTHOR = "Fabio 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 = "522534",
YEAR = "2008"
} 
