On Some Theoretic Aspects of Fuzzy Subsets

Abstract

This article proposes some important theoretic aspects of -fuzzy power set of a finite set. Here, we take a non-empty fi-nite set and an ordered subset of the closed interval , then the set of mappings from to denoted by is defined as -fuzzy power set. Considering the disjunctive union ‘ ’ operations between fuzzy subsets of , the struc-ture forms a groupoid, which is defined as special fuzzy groupoid. Later, we try to introduce the product of special fuzzy groupoids and their properties.

Introduction

Conclusion

The proposed work presented some important properties of -fuzzy power set. Considering the disjunctive union ‘ ’ op-erations between two fuzzy subsets of the -fuzzy power set, it forms a groupoid, which is defined as special fuzzy groupoid. Throughout this article different properties of the -fuzzy power set and special fuzzy groupoid are studied. We hope the results established in this article would find some applications and enrich the theory of fuzzy algebra.

References

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Copyright

Copyright © 2023 Dr. Sisir Kumar Rajbongshi, Prasanta Gogoi. 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.