On the action of a fuzzy group on a fuzzy set

Abstract

In this paper, we develop fundamental concepts required to extend the concept of group action on a set to fuzzy domain. We define product of a fuzzy set and a fuzzy group by using the idea of cartesian products of sets. We construct examples to demonstrate the defined concepts. We also discuss properties of the defined product of a fuzzy set and a fuzzy group as requisite to study of fuzzy group actions on fuzzy sets. Mathematics Subject Classification (2020). 08A99, 08C05, 22F05