Gómez González, DanielMontero De Juan, Francisco JavierYáñez Gestoso, Francisco JavierGonzález Pachón, J.Cutello, Vincenzo2023-06-202023-06-202004Gómez, D., Montero, J., Yáñez, J., González-Pachón, J., Cutello, V.: Crisp dimension theory and valued preference relations. International Journal of General Systems. 33, 115-131 (2004). https://doi.org/10.1080/030810703100016334910308-107910.1080/03081070310001633491https://hdl.handle.net/20.500.14352/50138In 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.engjournal articlehttps//doi.org/10.1080/03081070310001633491http://www.tandfonline.com/doi/pdf/10.1080/03081070310001633491restricted access519.8004.8Valued preference relationsDimension theoryPreference representationGeneralized dimension functionInteligencia artificial (Informática)Investigación operativa (Matemáticas)1203.04 Inteligencia Artificial1207 Investigación Operativa