*(English)*Zbl 0768.90003

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 $A$ of alternatives as follows: Strict preference: $aPb$ iff $aRb$ and not $bRa$; Indifference: $aIb$ iff $aRb$ and $bRa$; Incomparability: $aJb$ iff not $aRb$ and not $bRa$, where $R$ denotes a binary relation of weak preference, say $aRb$ iff $a$ is at least as good as $b$.

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.