Gomez, D. and Montero, 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

PDF
Restringido a Repository staff only hasta 2020. 232kB |

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 |
---|---|

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 |

References: | Adnadjevic, D. (1994) “Dimension of fuzzy ordered sets”, Fuzzy Sets and Systems 67, 349–357. Bouyssou, D., Marchant, T., Pirlot, M., Perny, P., Tsoukias, A. and Vincke, Ph. (2000) Evaluation and Decision Models (Kluwer, Dordrecht). Cutello, V. and Montero, J. (1994) “Fuzzy rationality measures”, Fuzzy Sets and Systems 62, 39–54. Doignon, J.P. and Mitas, J. (2000) “Dimension of valued relations”, European Journal of Operational Research 125, 571–587. Dushnik, B. and Miller, E.W. (1941) “Partially ordered sets”, American Journal of Mathematics 63, 600–610. Fodor, J.C. and Roubens, M. (1995) “Structure of valued binary relations”, Mathematical Social Sciences 30, 71–94. Gonzalez-Pachon, J. and Rios-Insua, S. (1999) “Mixture of maximal quasi orders: a new approach to preference modelling”, Theory and Decisions 47, 73–88. Gonzalez-Pachon, J., Gomez, D., Montero, J. and Yañez, J. (2003a) “Searching for the dimension of valued preference relations”, International Journal of Approximate Reasoning 33, 133–157. Gonzalez-Pachon, J., Go´mez, D., Montero, J. and Yañez, J. (2003b) “Soft dimension theory”, Fuzzy Sets and Systems 137, 137–149. Herrera, F., Herrera-Viedma, E. and Martinez, L. (2001) “A hierarchical ordinal model for managing unbalanced linguistic terms sets based on the linguistic 2-tuple model”, in Proceedings of the UROFUSE Workshop of Preference Modelling and Applications, (University of Granada, April 25–27), pp. 201–206. Macharis, C. and Brans, J.P. (1998) “The GDSS Promethee procedure”, Journal of Decision Systems 7, 283–307. Montero, J. (1987) “Arrow’s theorem under fuzzy rationality”, Behavioral Science 32, 267–273. Montero, J. and Tejada, J. (1986) “Some problems on the definition of fuzzy preference relations”, Fuzzy Sets and Systems 20, 45–53. Montero, J. and Cutello, V. (1994) “Fuzzy rationality measures”, Fuzzy Sets and Systems 62, 39–44. Montero, J., Ya´n˜ez, J., Cutello, V. (1998) “On the dimension of fuzzy preference relations”, in Proceedings of the ICSC International Symposium on Engineering of Intelligent Systems, (University of La Laguna), Vol. 3, pp. 38–33. Ovchinnikov, S.V. (1984) “Representation of transitive fuzzy relations”, In: Skala, H.J., Termini, S. and Trillas, E., eds, Aspects of Vagueness (Reidel, Amsterdam), pp 105–118. Roy, B. (1996) Multicriteria Methodology for Decision Aiding (Kluwer, Dordrecht). Szpilrajn, E. (1930) “Sur l’extension de l’ordre partiel”, Fundamenta Mathematicae 16, 386–389. Trotter, W. (1992) Combinatorics and Partially Ordered Sets. Dimension Theory (The Johns Hopkins University Press, Baltimore and London). Valverde, L. (1985) “On the structure of F-indistinguishability operators”, Fuzzy Sets and Systems 17, 313–328. Van de Walle, B. and Turoff, M. (2001) “Towards group agreement: the significance of preference analysis”, in Proceedings of the EUROFUSE Workshop of Preference Modelling and Applications, (University of Granada, April 25–27) pp. 85–92. Yannakakis, M. (1982) “On the complexity of the partial order dimension problem”, SIAM Journal of Algebra and Discrete Mathematics 3, 351–358. Yañez, J. and Montero, J. (1999) “A poset dimension algorithm”, Journal of Algorithms 30, 185–208. Zadeh, L.A. (1971) “Similarity relations and fuzzy orderings”, Information Sciences 3, 177–200. |

Deposited On: | 11 Oct 2012 09:29 |

Last Modified: | 19 Apr 2016 14:37 |

Repository Staff Only: item control page