A study on fundamentals of refined intuitionistic fuzzy set with some properties

Journal Title: Journal of Fuzzy Extension & Applications - Year 2020, Vol 1, Issue 4

Abstract

Zadeh conceptualized the theory of fuzzy set to provide a tool for the basis of the theory of possibility. Atanassov extended this theory with the introduction of intuitionistic fuzzy set. Smarandache introduced the concept of refined intuitionistic fuzzy set by further subdivision of membership and non-membership value. The meagerness regarding the allocation of a single membership and non-membership value to any object under consideration is addressed with this novel refinement. In this study, this novel idea is utilized to characterize the essential elements e.g. subset, equal set, null set, and complement set, for refined intuitionistic fuzzy set. Moreover, their basic set theoretic operations like union, intersection, extended intersection, restricted union, restricted intersection, and restricted difference, are conceptualized. Furthermore, some basic laws are also discussed with the help of an illustrative example in each case for vivid understanding.

Authors and Affiliations

Atiqe Ur Rahman; Muhammad Rayees Ahmad; Muhammad Saeed; Muhammad Ahsan; Muhammad Arshad; Muhammad Ihsan

Keywords

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  • EP ID EP692664
  • DOI 10.22105/JFEA.2020.261946.1067
  • Views 96
  • Downloads 0

How To Cite

Atiqe Ur Rahman; Muhammad Rayees Ahmad; Muhammad Saeed; Muhammad Ahsan; Muhammad Arshad; Muhammad Ihsan (2020). A study on fundamentals of refined intuitionistic fuzzy set with some properties. Journal of Fuzzy Extension & Applications, 1(4), -. https://europub.co.uk/articles/-A-692664