A Set-Valued Approach to Multiple Source Evidence

Abstract

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.