Counting fuzzy subgroups of some finite groups by a new equivalence relation

The study concerning the classification of the fuzzy subgroups of finite groups is a significant aspect of fuzzy group theory. In early papers, the number of distinct fuzzy subgroups of some nonabelian groups is calculated by the natural equivalence relation. In this paper, we treat to classifying fuzzy subgroups of some groups by a new equivalence relation which has a consistent group theoretical foundation. In fact, we determine exact number of fuzzy subgroups of finite non-abelian groups of order p3 and special classes of dihedral groups.