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

In this paper a new equivalence relation for classifying the fuzzy subgroups of finite groups is introduced and studied. This generalizes the equivalence relation defined on the lattice of fuzzy subgroups of a finite group that has been used in our previous papers. Explicit formulas for the number of distinct fuzzy subgroups with respect to the new equivalence relation are obtained in some particular cases.