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Belief and Plausibility Functions on Intuitionistic Fuzzy Sets
Author(s) -
Hwang ChaoMing,
Yang MiinShen
Publication year - 2016
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.21794
Subject(s) - generalization , mathematics , type 2 fuzzy sets and systems , fuzzy measure theory , fuzzy set , belief structure , artificial intelligence , fuzzy classification , fuzzy set operations , membership function , representation (politics) , fuzzy logic , fuzzy number , computer science , algebra over a field , discrete mathematics , pure mathematics , mathematical analysis , politics , political science , law
Belief and plausibility functions based on Dempster–Shafer theory have been used to measure uncertainty. They are also widely studied and applied in diverse areas. Numerous studies in the literature have presented various generalizations of belief and plausibility functions to fuzzy sets. However, there are still less generalizations of belief and plausibility functions to intuitionistic fuzzy sets. Because intuitionistic fuzzy sets can present the degrees of both membership and nonmembership with a degree of hesitancy, the knowledge and semantic representation becomes more general and applicable than fuzzy sets. In this paper, we propose a generalization of belief and plausibility functions to intuitionistic fuzzy sets based on fuzzy integral. Some numerical examples show the effectiveness of the proposed generalization. Furthermore, this generalization of belief and plausibility functions to intuitionistic fuzzy sets is able to catch more information about the change of intuitionistic fuzzy focal elements.