Approximating fuzzy preorders and equivalences. A similarity based approach

Although Fuzzy Preorders and Fuzzy Equivalences are intended to model vague concepts, they are defined in terms of properties or axioms to be fulfilled in a crisp way. In this paper we present two different approaches to overcome this problem (the axiomatic and the similarity based approaches) and relate them both. New results concerning the similarity between relational structures are obtained. As a consequence, every arbitrary fuzzy relation will be considered to be a fuzzy preorder or a fuzzy equivalence, at least to some extent.