A Set-Valued Approach to Multiple Source Evidence

Didier Dubois (1, 2) , Henri Prade (3, 1, 2)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 CNRS - Centre National de la Recherche Scientifique
3 UTS - University of Technology Sydney

This short note studies a multiple source extension of categorical mass functions in the sense of Shafer’s evidence theory. Each subset of possible worlds is associated with a subset of information sources and represents a tentative description of what is known. Analogs of belief, plausibility, commonality functions, valued in terms of subsets of agents or sources, are defined, replacing summation by set union. Set-valued plausibility is nothing but set-valued possibility because it is union-decomposable with respect to the union of events. In a special case where each source refers to a single information item, set-valued belief functions decompose with respect to intersection and are thus multiple source necessity-like function. Connections with Belnap epistemic truth-values for handling multiple source inconsistent information are shown. A formal counterpart of Dempster rule of combination is defined and discussed as to its merits for information fusion.

Mots clés: Multiple source extension; Shafer’s evidence theory; Belnap epistemic truth-values; Dempster rule of combination; Subsets; Categorical mass functions

Domaines: Algorithme et structure de données [cs.DS]; Apprentissage [cs.LG]

Didier Dubois, Henri Prade. A Set-Valued Approach to Multiple Source Evidence. 30th International Conference on Industrial Engineering and Other Applications of Applied Intelligent Systems (IEA/AIE), Jun 2017, Arras, France. pp.113-118. ⟨hal-02619446⟩