Publication: Decomposing preference relations
Full text at PDC
Advisors (or tutors)
IEEE,electron devices soc &reliability group
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.
IEEE International Conference on Fuzzy Systems JUL 23-26, 2007
D. Bouyssou, T. Marchant, M. Pirlot, P. Perny, A. Tsoukias and Ph. Vincke, Evaluation and Decision Models, Kluwer, Dordrecht, 2000. V. Cutello and J. Montero, "Fuzzy rationality measures", Fuzzy Sets and Systems 62:39-44, 1994. V. Cutello and J. Montero, "Equivalence and compositions of uzzyrationality measures", Fuzzy Sets and Systems 85:31-43, 1997. B. Dushnik and E.W. Miller, "Partially ordered sets",American Journal of Mathematics 63:600-610, 1941. D. Gomez, V. Lopez and J. Montero, "The role of fuzziness in decision making". In D. Ruan, E. Kerre and P. Wang, eds., Fuzzy Logic: an spectrum of applied and theoretical issues, Springer, in press. D. Gomez, J. Montero and J. Yanez (2006): A coloring algorithm for image classification. Information Sciences 176, 3645-3657. D. Gomez, J. Montero, J. Yanez, C. Poidomani (2007): A graph coloring algorithm approach for image segmentation. Omega 35:173-183. D. Gomez, J. Montero and J. Yanez, "Measuring criteria weights by means of dimension theory", Mathware and Soft Computing, in press. J. Gonzalez-Pachon, D. Gomez, J. Montero and J.Yanez, "Searching for the dimension of binary valued preference relations", Int. J. Approximate Reasoning 33:133-157, 2003. J. Gonzalez-Pachon, D.Gomez, J. Montero and J. Yanez, "Soft dimension theory", Fuzzy Sets and Systems 137:137-149, 2003. J. Montero, D. Gomez, J. Yanez amd J. Gonzalez-Pachn, "Rationality cores in preference representation", Proceedings IFSA'03 conference,Bogaziai University, Istambul; pp. 340-343, 2003 J. Montero and J. Tejada, "Some problems on the definition of fuzzy preference relation", Fuzzy Sets and Systems 20:45-53, 1986. P.K. Pattanaik, Voting and Collective Choice, Cambridge U.P., London,1971. B. Roy, "Decision sciences or decision aid sciences", European Journal of Operational Research 66:184-203, 1993. A.K. Sen, Collective Choice and Social Welfare, Holden-Day, San Francisco, 1970. W.T. Trotter, Combinatorics and Partially Ordered Sets. Dimension Theory, The Johns Hopkins University Press, Baltimore, 1992. M. Yannakakis, "On the complexity of the partial order dimension problem", SIAM Journal of Algebra and Discrete Mathematics 3:351-358, 1982. J. Yanez and J. Montero, "A poset dimension algorithm", Journal of Algorithms 30:185-208, 1999.