Semantics for Reciprocal Preferences
Fabián Castiblanco, Camilo A. Franco, J. Tinguaro Rodríguez, Javier Montero · Atlantis studies in uncertainty modelling/Atlantis Studies in Uncertainty Modelling · 2021
Examining fuzzy preference relations together with the reciprocity condition, and a potential conceptual conflict arising between reciprocal fuzzy preferences and fuzzy preference structures, it is claimed that reciprocal preferences cannot be properly understood according to a weak nor a strict preference predicate.Therefore, as the elements of a standard preference structure, namely strict preference, weak preference, indifference and incomparability, cannot be properly distinguished from reciprocal fuzzy preferences, the concept of lack of preference emerges as a natural category, in fact allowing to understand reciprocal fuzzy preferences according to the standard fuzzy preference model.Furthermore, the basic notion of lack of preference is shown to group all the non-preference relations into a basic, unifying concept, providing an adequate decomposition of the meaning of any reciprocal fuzzy preference relation.