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Belief, plausibility, and probability measures on interval‐valued type 2 fuzzy sets
Author(s) -
Türkşen I. Burhan
Publication year - 2004
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.20018
Subject(s) - mathematics , interval (graph theory) , axiom , type (biology) , measure (data warehouse) , fuzzy set , fuzzy logic , discrete mathematics , probability measure , set (abstract data type) , fuzzy measure theory , representation (politics) , analogy , fuzzy number , combinatorics , artificial intelligence , computer science , data mining , ecology , biology , linguistics , philosophy , geometry , politics , political science , law , programming language
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.