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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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.
|Uncontrolled Keywords:||Multicriteria decision analysis; Valued relations; Dimension theory|
|Subjects:||Sciences > Computer science > Artificial intelligence|
D. Adnadjevic, Dimension of fuzzy ordered sets, Fuzzy Sets and Systems 67 (1994) 349–357.
V. Belton, J. Hodgkin, Facilitators, decision makers, DIY users: Is intelligent multicriteria
decision support for all feasible or desirable? European Journal of Operational Research 113 (1999) 247–260.
V. Cutello, J. Montero, Fuzzy rationality measures, Fuzzy Sets and Systems 62 (1994) 39–54.
J.P. Doignon, J. Mitasm, Dimension of valued relations, European Journal of Operational Research 125 (2000) 571–587.
B. Dushnik, E.W. Miller, Partially ordered sets, American Journal of Mathematics 63 (1941)600–610.
J.C. Fodor, M. Roubens, Structure of valued binary relations, Mathematical Social Sciences 30 (1995) 71–94.
J. Gonzalez-Pachon, D. Gomez, J. Montero, J. Yañez, Soft dimension theory, Fuzzy Sets and Systems, in press [doi:10.1016/S0165-0114(02)00437-2].
J. Gonzalez-Pachon, S. Rios-Insua, A method for searching rationality in pairwise choices, in: G. Fandel, T. Gal (Eds.), Multiple Criteria Decision Making, Lecture Notes in Economics and Mathematical Systems, vol. 448, Springer, 1997, pp. 374–382.
J. Gonzalez-Pachon, S. Rios-Insua, Mixture of maximal quasi orders: a new approach to preference modelling, Theory and Decisions 47 (1999) 73–88.
C. Macharis, J.P. Brans, The GDSS promethee procedure, Journal of Decision Systems 7 (1998) 283–307.
J. Montero, Arrows theorem under fuzzy rationality, Behavioral Science 32 (1987) 267–273.
J. Montero, J. Yañez, V. Cutello, On the dimension of fuzzy preference relations, in: Proceedings International ICSC Symposium on Engineering of Intelligent Systems, La Laguna, vol. 3, 1998, pp. 38–33.
J. Montero, J. Yañez, D. Gomez, J. Gonzalez-Pachon, Consistency in dimension theory, in: Proceedings of the Workshop on Preference Modelling and Applications, Granada, 2001, pp.93–98.
S.V. Ovchinnikov, Representation of transitive fuzzy relations, in: H.J. Skala, S. Termini, E. Trillas (Eds.), Aspects of Vagueness, Reidel, Amsterdam, 1984, pp. 105–118.
P.K. Pattanaik, Voting and Collective Choice, Cambridge University Press, London, 1971.
B. Roy, Decision aid and decision making, European Journal of Operational Research 45 (1990) 324–331.
A.K. Sen, Collective Choice and Social Welfare, Holden-Day, San Francisco, 1970.
G. Shafer, Savage revisited (with discussion), Statistical Science 1 (1986) 435–462.
Y. Siskos, A. Spyridakos, Intelligent multicriteria decision support: overview and perspectives, European Journal of Operational Research 113 (1999) 236–246.
E. Szpilrajn, Sur l extension de l ordre partiel, Fundamenta Mathematicae 16 (1930) 386–389.
W.T. Trotter, Combinatorics and Partially Ordered Sets. Dimension Theory, The Johns Hopkins University Press, Baltimore, 1992.
L. Valverde, On the structure of F-indistinguishability operators, Fuzzy Sets and Systems 17 (1985) 313–328.
M. Yannakakis, On the complexity of the partial order dimension problem, SIAM Journal of Algebra and Discrete Mathematics 3 (1982) 351–358.
J. Yañez, J. Montero, A poset dimension algorithm, Journal of Algorithms 30 (1999) 185–208.
L.A. Zadeh, Similarity relations and fuzzy orderings, Informations Sciences 3 (1971) 177–200.
|Deposited On:||18 Oct 2012 12:43|
|Last Modified:||11 Oct 2013 15:27|
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