Characterization of fuzzy preference structures through Łukasiewicz triplets

Abstract

In this paper we characterize the reconstruction of a fuzzy set from its subsets by means of Lukasiewicz triplets. This result allows us to introduce a new definition of fuzzy strict preference, which is also satisfied in the crisp framework. The usual definitions of fuzzy indiference and fuzzy incomparability together with this one enable to construct and to characterize fuzzy preference structures from a reflexive fuzzy binary relation.