TitleBelief Functions on MV-algebras of Fuzzy Sets: An Overview
Publication TypeBook Chapter
Year of Publication2014
AuthorsFlaminio T, Godo L, Kroupa T
EditorY. Torra NV, Sugeno M.
Book TitleNon-Additive Measures

Belief functions are the measure theoretical objects Dempster-Shafer evidence theory is based on. They are in fact totally monotone capacities, and can be regarded as a special class of measures of uncertainty used to model an agent’s degrees of belief in the occurrence of a set of events by taking into account different bodies of evidence that support those beliefs. In this chapter we present two main approaches to extending belief func- tions on Boolean algebras of events to MV-algebras of events, modelled as fuzzy sets, and we discuss several properties of these generalized mea- sures. In particular we deal with the normalization and soft-normalization problems, and on a generalization of Dempster’s rule of combination.