Classical set theory formulated by George Cantor (1845-1918) is a versatile tool used to build mathematical models of various phenomena. In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition. The notion of a multiset is a generalization of the concept of a classical set which is obtained by relaxing restrictions of distinctness. In contrast to classical set theory, fuzzy set theory permits the gradual assessment of the membership of elements in a set which is described with the aid of a membership function valued in the real unit interval [0, 1]. Many real-world problems cannot be described and handled by the classical set theory, including all those involving elements with only partial membership of a set. Fuzzy set is a set with smooth boundary accepting partial memberships and therefore, in a sense generalizes the classical set theory. The broad objective of this paper is to explore the concept of classical sets and its extended versions of fuzzy sets and multisets. Fuzzy version of various algebraic structures like fuzzy groups and fuzzy modules are described with the help of basics of fuzzy sets.

classical set, fuzzy membership function, multiplicity of an element, fuzzy group.

Received: April 27, 2021; Accepted: May 17, 2021; Published: June 3, 2021

How to cite this article: Avinash J. Kamble, Harshada Pratham and Shital Rithe, A comprehensive survey: classical set to fuzzy set, Advances in Fuzzy Sets and Systems 26(1) (2021), 61-75. 10.17654/FS026010061

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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