The paper develops fuzzy set-based models for fundamental relations of strict preference, indifference, and incomparability. This generalization is aimed at preserving all classical properties found in preference modelling. Recall that in this theory the above binary relations are defined in a given family of alternatives as follows: Strict preference: iff and not ; Indifference: iff and ; Incomparability: iff not and not , where denotes a binary relation of weak preference, say iff is at least as good as .
The main results pertain to an extension of the classical results by proposing fuzzy models for the above relations. It is proved that a “reasonable” generalization (preserving the properties found in the Boolean case) should be based upon Lukasiewicz-like De Morgan triples.