Abstract
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.
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