FUZZY SUBGROUPS AND CERTAIN EQUIVALENCE RELATIONS

In this paper, we study an equivalence relation on the set of fuzzy subgroups of an arbitrary group G and give four equivalent conditions each of which characterizes this relation. We demonstrate that with this equivalence relation each equivalence class constitutes a lattice under the ordering of fuzzy set inclusion. Moreover, we study the behavior of these equivalence classes under the action of a group homomorphism.