CHARACTERIZABLE FUZZY PREFERENCE STRUCTURES

In this paper, we study the existence, construction and reconstruction of fuzzy preference structures. Starting from the definition of a cla ssical preference structure, we propose a natural definition of a fuzz y preference structure, merely requiring the fuzzification of the set operations involved. Upon evaluating the existence of these structures , we discover that the idea of fuzzy preferences is best captured when fuzzy preference structures are defined using a Lukasiewicz triplet. We then proceed to investigate the role of the completeness condition in these structures. This rather extensive investigation leads to the proposal of a strongest completeness condition, and results in the def inition of a one-parameter class of fuzzy preference structures. Invok ing earlier results by Fodor and Roubens, the construction of these st ructures from a reflexive binary fuzzy relation is then easily obtaine d. The reconstruction of such a structure from its fuzzy large prefere nce relation - inevitable to obtain a full characterization of these s tructures in analogy to the classical case - is more cumbersome. The m ain result of this paper is the discovery of a non-trivial characteriz ing condition that enables us to fully characterize the members of a t wo-parameter class of fuzzy preference structures in terms of their fu zzy large preference relation. As a remarkable side-result, we discove r three limit classes of characterizable fuzzy preference structures, traces of which are found throughout the preference modelling literatu re.