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Docta Complutense author González Pachón, J. author Gómez González, Daniel author Montero De Juan, Francisco Javier author Yáñez Gestoso, Francisco Javier 2023-06-20T16:59:56Z 2023-06-20T16:59:56Z 2003 González-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)00437-2 0165-0114 10.1016/S0165-0114(02)00437-2 https://hdl.handle.net/20.500.14352/57597 https//doi.org/10.1016/S0165-0114(02)00437-2 http://www.sciencedirect.com/science/article/pii/S0165011402004372 Classical 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. eng Soft dimension theory journal article URL https://docta.ucm.es/bitstreams/068b5f4e-e37f-4a70-9b01-75381168af96/download File MD5 f43b79ad454a58008f32cc2bf43af318 239670 application/pdf Montero47.pdf