Decomposition of fuzzy relations: An application to fuzzy preferences

In this article, working in the spirit of the classical Arrovian models in the fuzzy setting and their possible extensions, we go deeper into the study of some type of decompositions defined by t-norms and t-conorms. This allows us to achieve characterizations of existence and uniqueness for such decompositions and we provide rules to obtain them under some specific conditions. We conclude by applying such results to the study of fuzzy preferences, a key concept in Fuzzy Social Choice

Factorization of fuzzy preferences

Producción CientíficaIn the ordinary framework, the factorization of a weak preference relation into a strict preference relation and an indifference relation is unique. However, in fuzzy set theory, the intersection and the union of fuzzy sets can be represented different ways. Furthermore, some equivalent properties in the ordinary case have generalizations in the fuzzy framework that may be not equivalent. For these reasons there exist in the literature several factorizations of a fuzzy weak preference relation. In this paper we obtain and characterize different factorizations of fuzzy weak preference relations by means of two courses of action which are equivalent in the ordinary framework: axioms and definitions of strict preference and indifference.Ministerio de Ciencia y Tecnología (Proyecto BEC2001-2253) and FEDERJunta de Castilla y León (Consejería de Educación y Cultura, Proyecto VA057/02