Fuzzy probabilities: tentative discussions on the mathematical concepts

Authors:
Enric Trillas;Takehiko Nakama;Itziar García-Honrado
Affiliations:
European Center for Soft Computing, Edificio Científico-Technológico, Mieres, Asturias, Spain;European Center for Soft Computing, Edificio Científico-Technológico, Mieres, Asturias, Spain;European Center for Soft Computing, Edificio Científico-Technológico, Mieres, Asturias, Spain
Venue:
IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
Year:
2010

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Abstract

Various forms of probability and probabilistic concepts have been discussed in fuzzy logic since its very inception, but their mathematical foundations have yet to be fully established. In this paper, we investigate theoretical issues concerning (1) probability measures as membership functions, (2) probability measures for fuzzy sets, and (3) fuzzy-valued probabilities.