A Purview and the inter-relations of “Fuzzy Sets, Intuitionistic Fuzzy Sets, Rough Sets, and their Extensions”

Babita Mishra¹

1. Department of Mathematics, Mahatma Gandhi Central University, Motihari, India.

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.6 , pp.43-49, Dec-2022

Online published on Dec 31, 2022

Copyright © Babita Mishra . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
The handling of uncertainty and vagueness is a very tough task for any decision-making body. It is not possible to mathematically formulate a realistic problem by ignoring the terms like uncertain and vague. Therefore taking into consideration such types of linguistic variables, it is an essential tool for any decision-maker to handle such types of situations by using “fuzzy sets, intuitionistic fuzzy sets, rough sets, etc.” In this paper, I would like to define fuzzy sets and how gradually all the extensions or purview as a “rough set, type-2 fuzzy set, and intuitionistic fuzzy sets” are developed have been discussed. The outline of this paper includes historical development, definitions, and the relevance of the topic through real-world examples. The most important feature of this paper is to incorporate the same example in different extensions to understand the difference and needs of the extensions. Also, the inter-relations of all the sets (cited above) have been discussed.

Key-Words / Index Term :
Fuzzy sets, Rough set, Type-2 fuzzy set, Intuitionistic fuzzy sets, Uncertainty, Vagueness

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