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Belief functions on lattices
Author(s) -
Grabisch Michel
Publication year - 2009
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.20321
Subject(s) - function (biology) , computer science , combinatorics , citation , lattice (music) , discrete mathematics , epistemology , mathematical economics , philosophy , mathematics , library science , physics , evolutionary biology , acoustics , biology
We extend the notion of belief function to the case where the underlying structure is no more the Boolean lattice of subsets of some universal set, but any lattice, which we will endow with a minimal set of properties according to our needs. We show that all classical constructions and definitions (e.g., mass allocation, commonality function, plausibility functions, necessity measures with nested focal elements, possibility distributions, Dempster rule of combination, decomposition with regard to simple support functions, etc.) remain valid in this general setting. Moreover, our proof of decomposition of belief functions into simple support functions is much simpler and general than the original one by Shafer. © 2008 Wiley Periodicals, Inc.