Journal
IEEE TRANSACTIONS ON FUZZY SYSTEMS
Volume 22, Issue 2, Pages 420-436Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2013.2260549
Keywords
Consonant belief functions; geometric approach; isopignistic function; L-p norms; (outer) consonant approximation; possibility theory; simplicial complex; theory of evidence
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In this paper, we solve the problem of approximating a belief measure with a necessity measure or consonant belief function in a geometric framework. Consonant belief functions form a simplicial complex in both the space of all belief functions and the space of all mass vectors: Partial approximations are first sought in each component of the complex, while global solutions are selected among them. As a first step in this line of study, we seek here approximations that minimize L-p norms. Approximations in the mass space can be interpreted in terms of mass redistribution, while approximations in the belief space generalize the maximal outer consonant approximation. We compare them with each other and with other classical approximations and illustrate them with the help of a running example.
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