  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.
