Counting Distinct Fuzzy Subgroups of Symmetric Group S5 by a New Equivalence Relation

Abstract

One of the significant aspects of fuzzy group theory is a classification of the fuzzy subgroups of finite groups under a suitable equivalence relation. In this paper, we determine the number of distinct fuzzy subgroups of finite symmetric group S5 by the new equivalence relation introduced by Tărnăuceanu. In this case, the corresponding equivalence classes of fuzzy subgroups of a group G are closely connected to the automorphism group and the chains of subgroups of G.