Classifying and counting fuzzy normal subgroups by a new equivalence relation

Abstract

The main goal of this paper is to give an explicit formula for the number of fuzzy normal subgroups of some finite non-abelian groups by using the new equivalence relation presented in [Fuzzy Sets and Systems, 289 (2016) 113-121]. Precisely, for a group G this new equivalence is induced by an action of the automorphism group Aut(G) associated with G on the lattice of fuzzy normal subgroups of G. In fact, this new equivalence relation generalizes the natural equivalence relation defined on the lattice of fuzzy normal subgroups.