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Searching for the dimension of valued preference relations.

González-Pachón, J. and Gomez, D. and Montero de Juan, Francisco Javier and Yañez Gestoso, Francisco Javier (2003) Searching for the dimension of valued preference relations. International Journal of Approximate Reasoning, 33 (2). pp. 133-137. ISSN 0888-613X

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Abstract

The more information a preference structure gives, the more sophisticated representation techniques are necessary, so decision makers can have a global view of data and therefore a comprehensive understanding of the problem they are faced with. In this paper we propose to explore valued preference relations by means of a search for the number of underlying criteria allowing its representation in real space. A general representation theorem for arbitrary crisp binary relations is obtained, showing the difference in representation between incomparability-related to the intersection operator-and other inconsistencies-related to the union operator. A new concept of dimension is therefore proposed, taking into account inconsistencies in source of information. Such a result is then applied to each alpha-cut of valued preference relations. (C) 2002 Elsevier Science Inc. All rights reserved.


Item Type:Article
Uncontrolled Keywords:Multicriteria decision analysis; Valued relations; Dimension theory
Subjects:Sciences > Computer science > Artificial intelligence
ID Code:16727
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