Two Functional Equations in Fuzzy Preference Modelling

Preference modelling is a fundamental part of several applied fields but at the same time it has its own interesting theoretical problems. There exists a well-known axiomatic approach to fuzzy preference structures. In this axiomatic framework, general constructions of strict preference, indifference and incomparability relations associated with a fuzzy large preference relation are established via solving a system of functional equations. In the present paper we overview the solutions of two key functional equations (one of Frank, and one of Alsina) under different conditions on the underlying logic operations. Consequences of these general results to fuzzy preference modelling are also summarized