Belief, plausibility, and probability measures on interval-valued type 2 fuzzy sets

Belief (Bel), plausibility (Pl), and probability (P) measures can be formulated on interval‐valued type 2 fuzzy sets with their representation in terms of α‐level (crisp) sets. Recently, it was shown that interval‐valued type 2 fuzzy sets naturally arise with modified and restricted multivalued maps of Dempster. An analogy to Dempster's upper and lower probabilities, upper and lower beliefs, and Pl and P measures can be determined over interval‐valued type 2 fuzzy sets. It is shown that the application of appropriate t‐norms over α‐values of α‐level crisp sets in combination with the axiom of Bel measure entails appropriate weights for the overlapping α‐level (crisp) set conjunctions where Bel measure is applicable. © 2004 Wiley Periodicals, Inc.