Fuzzy subgroups: Some characterizations. II

Abstract We consider an analysis of fuzzy subgroups in terms of the corresponding family of level subgroups. Given a finite chain of subgroups of a group G , we prove that there exists a fuzzy subgroup of G whose level subgroups are exactly the subgroups of this chain. As a corollary we obtain an interpretation of the number of chains of subgroups of a group G in which a subgroup H is a member. When the group G is a supersolvable group, some further interpretation of this number is obtained.