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 ?-fuzzy dissimilarity relations as the counter part of ?-fuzzy equivalence relations. It is proved that these newly defined ?-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.

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