Some notes on equivalent fuzzy sets and fuzzy subgroups

Abstract

This paper discusses the problems of equivalent fuzzy sets and fuzzy subgroups. First, a critical discussion of previous results by Murali and Makamba is provided. Second, this paper discusses the conditions under which the equivalence relation of fuzzy sets can be equivalently described by their level sets. It also suggests that the equivalence approach to the classification of fuzzy subgroups is suitable only for finite groups and proposes a new definition for the classification of fuzzy subgroups "S*-equivalence", showing that any two fuzzy subgroups of an infinite cyclic group with infinite membership values are S*-equivalent.