A Note on Fuzzy Automorphism and Inner Automorphism of Groups
Shiv Narain, Sunil Kumar, Sandeep Kumar, Gaurav Mittal

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.
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Taxonomy
TopicsFuzzy and Soft Set Theory · Fuzzy Logic and Control Systems · Fixed Point Theorems Analysis
