On the characterization of fuzzy preference structures

The characterization of preference structures constitutes an essential part in the study of preference modelling. A crisp preference structure can be characterized by the union of its relation of strict preference and its relation of indifference. It also can be characterized by the union of its relation of strict preference and its relation of incomparability. The last characterization is not useful in practice and it is less studied in the literature. In this paper, we study the conditions on the components of a fuzzy preference structure under which this fuzzy preference structure can be characterized by the W′ϕ-union of its relation of strict preference and its relation of indifference where ⟨Wϕ,W′ϕ,Nϕ⟩ is the De Morgan triplet modelling the classical De Morgan triplet ⟨and, or, not⟩.