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González-Pachón, J. and Gomez, D. and Montero, Javier and Yáñez, Javier
(2003)
*Soft dimension theory.*
Fuzzy Sets and Systems, 137
(1).
pp. 137-149.
ISSN 0165-0114

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Official URL: http://www.sciencedirect.com/science/article/pii/S0165011402004372

## Abstract

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.

Item Type: | Article |
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Uncontrolled Keywords: | Multicriteria decision analysis; Dimension theory; Fuzzy preference relations. |

Subjects: | Sciences > Mathematics > Operations research Sciences > Mathematics > Logic, Symbolic and mathematical |

ID Code: | 16725 |

Deposited On: | 18 Oct 2012 10:47 |

Last Modified: | 21 Jun 2018 10:27 |

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