A new equivalence relation to classify the fuzzy subgroups of finite groups

TL;DR

This paper introduces a new equivalence relation for classifying fuzzy subgroups of finite groups, generalizing previous relations, and provides explicit formulas for counting distinct fuzzy subgroups in certain cases.

Contribution

It proposes a novel equivalence relation to classify fuzzy subgroups, extending existing methods, and derives explicit formulas for specific cases.

Findings

New equivalence relation $ ewrel$ introduced

Explicit formulas for counting fuzzy subgroups derived

Generalizes previous classification methods

Abstract

In this paper a new equivalence relation $\approx$ to classify the fuzzy subgroups of finite groups is introduced and studied. This generalizes the equivalence relation $\sim$ defined on the lattice of fuzzy subgroups of a finite group that has been used in our previous papers (see e.g. \cite{16,24}). Explicit formulas for the number of distinct fuzzy subgroups with respect to $\approx$ are obtained in some particular cases.