In this paper a new equivalence relation $\approx$ to classify the fuzzysubgroups of finite groups is introduced and studied. This generalizes theequivalence relation $\sim$ defined on the lattice of fuzzy subgroups of afinite 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.
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