期刊
IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS
卷 37, 期 4, 页码 993-1008出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSMCB.2007.895991
关键词
bayesian belief functions (b.f.); commutativity; geometric approach; intersection probability; orthogonal projection; theory of evidence
In this paper, we analyze from a geometric perspective the meaningful relations taking place between belief and probability functions in the framework of the geometric approach to the theory of evidence. Starting from the case of binary domains, we identify and study three major geometric entities relating a generic belief function (b.f.) to the set of probabilities P: 1) the dual line connecting belief and plausibility functions; 2) the orthogonal complement of P; and 3) the simplex of consistent probabilities. Each of them is in turn associated with a different probability measure that depends on the original b.f. We focus in particular on the geometry and properties of the orthogonal projection of a b.f. onto P and its intersection probability, provide their interpretations in terms of degrees of belief, and discuss their behavior with respect to affine combination.
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