RT Book, Section T1 Decomposing preference relations A1 Gómez González, Daniel A1 Montero De Juan, Francisco Javier A1 Yáñez Gestoso, Francisco Javier AB In this paper we address the problem of inconsistency in preference relations, pointing out the relevance of a meaningful representation in order to help decision maker to capture such inconsistencies. Dimension theory framework, despite its computational complexity, is considered here, pursuing in principle a decomposition of arbitrary preference relations in terms of linear orderings of alternatives. But we shall then stress that consistency should not be necessarily associated to a linear ordering. In this way, alternative decompositions of a preference relation can be proposed to decision maker, allowing an effective search for a useful representations of alternatives in terms of possible criteria. Such decompositions of our preference relations will then become the basis of a future decision aid model, always with the restricted aim of allowing the decision maker a better understanding of the problem. Inconsistencies may be not simply suppressed but understood, since they may contain relevant information. PB IEEE,electron devices soc &reliability group SN 978-1-4244-1209-9 YR 2007 FD 2007 LK https://hdl.handle.net/20.500.14352/53163 UL https://hdl.handle.net/20.500.14352/53163 LA eng NO IEEE International Conference on Fuzzy SystemsJUL 23-26, 2007 DS Docta Complutense RD 19 abr 2025