On the relationship between fuzzy subgroups and indistinguishability operators

Abstract

Fuzzy subgroups are revisited considering their close relationship with indistinguishability operators (fuzzy equivalences) invariant under translations. Different ways to obtain new fuzzy subgroups from a given one are provided and different ways to characterize normal fuzzy subgroups are obtained. The idea of double coset of two (crisp) subgroups allows us to relate them via their equivalence classes. This is generalized to the fuzzy framework. The conditions in which a fuzzy relation R on a group G can be considered a fuzzy subgroup of G×G are obtained.