A Note on Fuzzy Automorphism and Inner Automorphism of Groups

TL;DR

This paper extends classical group theory concepts to fuzzy groups, introducing fuzzy automorphisms and fuzzy inner automorphisms, and derives fuzzy analogues of established results.

Contribution

It introduces fuzzy automorphisms and fuzzy inner automorphisms, extending classical group theory to fuzzy groups with new theoretical results.

Findings

Defined fuzzy inner automorphisms

Established fuzzy analogues of classical results

Extended endomorphism concepts to fuzzy automorphisms

Abstract

The fuzzification of classical set theory came into existence when Zadeh [1] laid down the concept of a fuzzy set as a generalization of a crisp set. The objective of this paper is to extend the concept of fuzzy endomorphism to fuzzy automorphism. Notions of fuzzy inner automorphism and fuzzy inner automorphism induced by a fuzzy subgroup are introduced. Finally, we obtain the fuzzy analogues of well-known results of classical group theory.