Belief functions on lattices

Abstract : 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 w.r.t. 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.
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Article dans une revue
International Journal of Intelligent Systems, Wiley, 2009, 24 (1), pp.76-95. 〈10.1002/int.20321〉
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Contributeur : Michel Grabisch <>
Soumis le : jeudi 20 novembre 2008 - 16:51:01
Dernière modification le : mardi 27 mars 2018 - 11:48:05
Document(s) archivé(s) le : lundi 7 juin 2010 - 21:47:45


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Michel Grabisch. Belief functions on lattices. International Journal of Intelligent Systems, Wiley, 2009, 24 (1), pp.76-95. 〈10.1002/int.20321〉. 〈hal-00340378〉



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