Fuzzy dissimilarity and generalization of Valverde's theorem on T-indistinguishability relations

Similarity and dissimilarity between fuzzy sets are popular notions in decision making problems. This paper studies the representations of ϵ-fuzzy dissimilarity relations as the counter part of ϵ-fuzzy equivalence relations. It is proved that these newly defined ϵ-fuzzy dissimilarity relations satisfy the axioms of self dissimilarity and symmetry along with certain inequalities which transform into Valverde's representation theorem in the particular case when the given relation is 1-fuzzy transitive.