González Pachón, J.Gómez González, DanielMontero De Juan, Francisco JavierYáñez Gestoso, Francisco Javier2023-06-202023-06-202003González-Pachón, J., Gómez, D., Montero, J., Yáñez, J.: Searching for the dimension of valued preference relations. International Journal of Approximate Reasoning. 33, 133-157 (2003). https://doi.org/10.1016/S0888-613X(02)00150-00888-613X10.1016/S0888-613X(02)00150-0https://hdl.handle.net/20.500.14352/57598The more information a preference structure gives, the more sophisticated representation techniques are necessary, so decision makers can have a global view of data and therefore a comprehensive understanding of the problem they are faced with. In this paper we propose to explore valued preference relations by means of a search for the number of underlying criteria allowing its representation in real space. A general representation theorem for arbitrary crisp binary relations is obtained, showing the difference in representation between incomparability-related to the intersection operator-and other inconsistencies-related to the union operator. A new concept of dimension is therefore proposed, taking into account inconsistencies in source of information. Such a result is then applied to each alpha-cut of valued preference relations. (C) 2002 Elsevier Science Inc. All rights reserved.engjournal articlehttps//doi.org/10.1016/S0888-613X(02)00150-0http://www.sciencedirect.com/science/article/pii/S0888613X02001500open access004.8Multicriteria decision analysisValued relationsDimension theoryInteligencia artificial (Informática)1203.04 Inteligencia Artificial