In this paper a new equivalence relation for classifying the fuzzy subgroups of finite groups is studied. Without any equivalence relation on fuzzy subgroups of group G, the number of fuzzy subgroups is infinite, even for the trivial group. The number of distinct fuzzy subgroups with respect to the new equivalence relation is obtained for S4.
The aim of this paper is to classify the fuzzy subgroups of the alternating group. First, an equivalence relation on *the set of all fuzzy subgroups of a group G is defined. Without any equivalence relation on fuzzy subgroups of group G, the number of fuzzy subgroups is infinite, even for the trivial group. Explicit formulae for the number of distinct fuzzy subgroup of finite alternating group are obtained in the particular case n = 5. Some inequalities satisfied by this number are also established for n≥ 5.
