RT Journal Article
T1 Soft dimension theory
A1 González Pachón, J.
A1 Gómez González, Daniel
A1 Montero De Juan, Francisco Javier
A1 Yáñez Gestoso, Francisco Javier
AB 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.
PB Elsevier Science Bv
SN 0165-0114
YR 2003
FD 2003
LK https://hdl.handle.net/20.500.14352/57597
UL https://hdl.handle.net/20.500.14352/57597
LA eng
NO 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
DS Docta Complutense
RD 18 abr 2025