On the fuzzification of semiorders

The class of semiorders is one of the most studied classes of crisp preference structures without incomparability in classical preference modelling. In this paper we propose a generalisation of the classical definitions of semiorder and strict semiorder to the case of fuzzy binary relations. We focus our attention on semiorders and strict semiorders defined by means of min–max De Morgan triplets and Lukasiewicz De Morgan triplets.