Abstract
AbstractFuzzy sets have a great progress in every scientific research area. It found many application areas in both theoretical and practical studies from engineering area to arts and humanities, from computer science to health sciences, and from life sciences to physical sciences. In this paper, a comprehensive literature review on the fuzzy set theory is realized. In the recent years, ordinary fuzzy sets have been extended to new types and these extensions have been used in many areas such as energy, medicine, material, economics and pharmacology sciences. This literature review also analyzes the chronological development of these extensions. In the last section of the paper, we present our interpretations on the future of fuzzy sets.
Highlights
A fuzzy set is a class of objects whose memberships are not precisely defined [1]
Along with the emergence of the fuzzy set theory, many objections to the theory have appeared [3]. Those brilliant scientists could not accept Zadeh’s way of handling the uncertainty. They so much exaggerated in decrying it that the logic of the theory was defined as “Fuzzy logic is the cocaine of science." the fuzzy logic proved its power through the real technology applications
Even the fuzzy set theory is a young theory, whose age is only 50; it has covered a lot of ground by today
Summary
A fuzzy set is a class of objects whose memberships are not precisely defined [1]. Fuzzy sets provide a better representation of reality than the classical mathematical binary representation. Along with the emergence of the fuzzy set theory, many objections to the theory have appeared [3] Those brilliant scientists could not accept Zadeh’s way of handling the uncertainty. A comprehensive literature review for the fuzzy set theory is realized It aims at exhibiting the expansion areas of the fuzzy set theory in its 50th year and presents the results of literature review with graphical illustrations and a classification with respect to the extensions of fuzzy sets. It is the most comprehensive and up to date literature review of the fuzzy set theory.
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