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Crisp dimension theory and valued preference relations.

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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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
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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