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

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.