Belief, plausibility, and probability measures on interval‐valued type 2 fuzzy sets | Zendy

Türkşen I. Burhan | Zendy

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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.

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