Journal
IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART C-APPLICATIONS AND REVIEWS
Volume 38, Issue 4, Pages 522-534Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSMCC.2008.919174
Keywords
belief function (b.f.); belief space; conditional subspace; Dempster's rule; simplex; theory of evidence (ToE)
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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 (b.f.) and Dempster's sum. On one side, we analyze the geometry of b.f.'s 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 are able to depict the geometric structure of conditional subspaces, i.e., sets of b.f.'s conditioned by a given function b. Natural applications of these geometric methods to classical problems such as probabilistic approximation and canonical decomposition are outlined.
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