On fuzzy preference relations

Abstract

Triangular norms, conorms, and negation functions are used as interpretations for propositional connectives in a multiple-valued logic model for fuzzy binary relations of weak preference, strict preference, and indifference. It is shown that the Law of Contradiction is a necessary condition for the very existence of reflexive transitive fuzzy binary relations. Basic properties of indifference and strict preference relations are established including transitivity of a strict preference.