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.: Soft dimension theory. Fuzzy Sets and Systems. 137, 137-149 (2003). https://doi.org/10.1016/S0165-0114(02)00437-20165-011410.1016/S0165-0114(02)00437-2https://hdl.handle.net/20.500.14352/57597Classical dimension theory, when applied to preference modeling, is based upon the assumption that linear ordering is the only elemental notion for rationality. In fact, crisp preferences are in some way decomposed into basic criteria, each one being a linear order. In this paper, we propose that indeed dimension is relative to a previous idea of rationality, but such a rationality is not unique. In particular, we explore alternative approaches to dimension, based upon a more general representation and allowing different classes of orders for basic criteria. In this way, classical dimension theory is generalized. As a first consequence, we explore the existence of crisp preference representations not being based upon linear orders. As a second consequence, it is suggested that an analysis of valued preference relations can be developed in terms of the representations of all alpha-cuts.engjournal articlehttps//doi.org/10.1016/S0165-0114(02)00437-2http://www.sciencedirect.com/science/article/pii/S0165011402004372restricted access519.83510.64Multicriteria decision analysisDimension theoryFuzzy preference relations.Investigación operativa (Matemáticas)Lógica simbólica y matemática (Matemáticas)1207 Investigación Operativa1102.14 Lógica Simbólica