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oai:docta.ucm.es:20.500.14352/531632024-11-25T16:31:36Zcom_20.500.14352_14col_20.500.14352_21

Decomposing preference relations Gómez González, Daniel Montero De Juan, Francisco Javier Yáñez Gestoso, Francisco Javier 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. 2023-06-20T13:38:31Z 2023-06-20T13:38:31Z 2023-06-20T13:38:31Z 2007 book part https://hdl.handle.net/20.500.14352/53163 XXXX-XXXX eng IEE monograph series TIN2006-06290. restricted access IEEE,electron devices soc &reliability group