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

Abstract

‎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 non-abelian 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 $p^3$ and special classes of dihedral groups‎.