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 = "522--534",
  YEAR = "2008" 
}

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