Belief Functions on MV-Algebras of Fuzzy Events Based on Fuzzy Evidence

Abstract

Recently Kroupa has proposed a generalization of belief functions on MV-algebras, the latter being the chosen algebraic setting for fuzzy (or many-valued) events. However, Kroupa's belief functions evaluate the degree of belief in the occurrence of fuzzy events by taking into account (weighted) evidence on classical subsets. In other words, the focal elements, used in determining the degree of belief, are classical sets. Within the MV-algebraic setting, the aim of the present work is to introduce a generalization of Kroupa belief functions that allows to deal with fuzzy events supported by evidence on fuzzy subsets.