Belief and Plausibility Functions on Intuitionistic Fuzzy Sets

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. C © 2015 Wiley Periodicals, Inc.