2026-07-30T08:00:59Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/575982024-11-25T16:23:46Zcom_20.500.14352_14col_20.500.14352_15

Searching for the dimension of valued preference relations González Pachón, J. Gómez González, Daniel Montero De Juan, Francisco Javier Yáñez Gestoso, Francisco Javier 004.8 Multicriteria decision analysis Valued relations Dimension theory Inteligencia artificial (Informática) 1203.04 Inteligencia Artificial The 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. Depto. de Estadística e Investigación Operativa Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T16:59:57Z 2023-06-20T16:59:57Z 2003 journal article https://hdl.handle.net/20.500.14352/57598 0888-613X 10.1016/S0888-613X(02)00150-0 eng González-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)00150-0 open access application/pdf Elsevier Science INC