Homomorphism of Characteristic Fuzzy Subgroup and Abelian Fuzzy Subgroup

Abstract

In this paper, we have established some independent proof of homomorphism on algebra of abelian and characteristic fuzzy subgroup. The characteristic of fuzzy subgroup [13] was first introduced by P. Bhattacharya and N. P. Mukharjee in 1986.

Introduction

I. INTRODUCTION

The concept of fuzzy sets was introduced by L.A.Zadeh [15] in 1965.Study of algebraic structure was first introduced by A.Rosenfeld [1]. After that a series of researches have done in this direction P.Bhattacharya and N.P.Mukharjee[13] have defined fuzzy normal subgroup and characteristic fuzzy subgroup in 1986. In this paper we have tried to established some independent proof about the properties of fuzzy group homomorphism on algebra of characteristic fuzzy subgroup.

II. PRELIMINARIES

In this section, we recall and study some concepts associated with fuzzy sets and fuzzy group, which we need in the subsequent sections.

A. Fuzzy Set

Over the past three decades, a number of definitions of a fuzzy set and fuzzy group have appeared in the literature (cf., e.g., [15, 1, 3, 7, 10]). In [15], it has been shown that some of these are equivalent. We begin with the following basic concepts of fuzzy set, fuzzy point and fuzzy group.

Conclusion

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Copyright

Copyright © 2022 Amit Kumar Arya, Dr. M. Z. Alam. 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.