A note on (∈, ∈∨q)-fuzzy equivalence relations and indistinguishability operators

Abstract

In this paper (∈ , ∈∨q)-fuzzy equivalence relations are defined and some of their properties are studied. The partition of an (∈ , ∈∨q)-fuzzy equivalence relation is studied. It is shown that under a semibal- anced mapping the preimage of an (∈ , ∈∨q)-fuzzy equivalence rela- tion is an (∈ , ∈∨q)-fuzzy equivalence relation, whereas the image of an (∈ , ∈∨q)-fuzzy equivalence relation under a balanced mapping is an (∈, ∈∨q)-fuzzy equivalence relation. To conclude, (∈ , ∈∨q)-fuzzy indistinguishability relations are defined and some of their properties are studied.