### Impacto

Gomez, D. and Montero de Juan, Francisco Javier and Yañez Gestoso, Francisco Javier and González-Pachón, J. and Cutello, V.
(2004)
*Crisp dimension theory and valued preference relations.*
International Journal of General Systems, 33
(2-3).
pp. 115-131.
ISSN 0308-1079

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Official URL: http://www.tandfonline.com/doi/pdf/10.1080/03081070310001633491

## Abstract

In this paper we address the problem of inconsistency in preference relations, pointing out the relevance of a meaningful representation in order to help decision maker to capture such inconsistencies. Dimension theory framework, despite its computational complexity, is considered here, pursuing in principle a decomposition of arbitrary preference relations in terms of linear orderings of alternatives. But we shall then stress that consistency should not be necessarily associated to a linear ordering. In this way, alternative decompositions of a preference relation can be proposed to decision maker, allowing an effective search for a useful representations of alternatives in terms of possible criteria. Such decompositions of our preference relations will then become the basis of a future decision aid model, always with the restricted aim of allowing the decision maker a better understanding of the problem. Inconsistencies may be not simply suppressed but understood, since they may contain relevant information.

Item Type: | Article |
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Uncontrolled Keywords: | Valued preference relations; Dimension theory; Preference representation; Generalized dimension function |

Subjects: | Sciences > Computer science > Artificial intelligence Sciences > Mathematics > Operations research |

ID Code: | 16679 |

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Deposited On: | 11 Oct 2012 09:29 |

Last Modified: | 07 Feb 2014 09:33 |

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