Biblioteca de la Universidad Complutense de Madrid

Soft dimension theory.


González-Pachón, J. y Gomez, D. y Montero, Javier y Yáñez, Javier (2003) Soft dimension theory. Fuzzy Sets and Systems, 137 (1). pp. 137-149. ISSN 0165-0114

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Classical dimension theory, when applied to preference modeling, is based upon the assumption that linear ordering is the only elemental notion for rationality. In fact, crisp preferences are in some way decomposed into basic criteria, each one being a linear order. In this paper, we propose that indeed dimension is relative to a previous idea of rationality, but such a rationality is not unique. In particular, we explore alternative approaches to dimension, based upon a more general representation and allowing different classes of orders for basic criteria. In this way, classical dimension theory is generalized. As a first consequence, we explore the existence of crisp preference representations not being based upon linear orders. As a second consequence, it is suggested that an analysis of valued preference relations can be developed in terms of the representations of all alpha-cuts.

Tipo de documento:Artículo
Palabras clave:Multicriteria decision analysis; Dimension theory; Fuzzy preference relations.
Materias:Ciencias > Matemáticas > Investigación operativa
Ciencias > Matemáticas > Lógica simbólica y matemática
Código ID:16725

D. Adnadjevic, Dimension off uzzy ordered sets, Fuzzy Sets and Systems 67 (1994) 349–357.

V. Cutello, J. Montero, Fuzzy rationality measures, Fuzzy Sets and Systems 62 (1994) 39–54.

J.P. Doignon, J. Mitas, Dimension ofvalued relations, European J. Oper. Res. 125 (2000) 571–587.

B. Dushnik, E.W. Miller, Partially ordered sets, Amer. J. Math. 63 (1941) 600–610.

J.C. Fodor, M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer, Dordrecht, 1994.

J.C. Fodor, M. Roubens, Structure ofvalued binary relations, Math. Soc. Sci. 30 (1995) 71–94.

M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.

J. Gonzalez-Pachon, D. Gomez, J. Montero, J. Yañez, Searching for the dimension of binary valued preference relations, Int. J. Approx. Reasoning (2003), to appear.

J. Gonzalez-Pachon, S. Rios-Insua, Mixture ofmaximal quasi orders: a new approach to preference modelling, Theory Decisions 47 (1999) 73–88.

C. Marichal, J.P. Brans, The GDSS promethee procedure, J. Decision Systems 7 (1998) 283–307.

J. Montero, Arrow’s theorem under fuzzy rationality, Behav. Sci. 32 (1987) 267–273.

J. Montero, J. Tejada, Some problems on the denition of fuzzy preference relation, Fuzzy Sets and Systems 20 (1986) 45–53.

J. Montero, J. Yañez, V. Cutello, On the dimension of fuzzy preference relations, in: Proc. Internat. ICSC Sympon.Engineering ofIntelligent Systems, vol. 3, University ofLa Laguna, 1998, pp. 28–33.

J. Montero, J. Yañez, D. Gomez, J. Gonzalez-Pachon, Consistency in dimension theory, in: Proc. Workshop on Preference Modelling and Applications, Granada, April 25–27, 2001, pp. 93–98.

S.V. Ovchinnikov, Representation oftransitive fuzzy relations, in: H.J. Skala, S. Termini, E. Trillas (Eds.),Aspects of Vagueness, Reidel, Amsterdam, 1984, pp. 105–118.

S.V. Ovchinnikov, M. Roubens, On strict preference relations, Fuzzy Sets and Systems 43 (1991) 319–326.

M. Roubens, Ph. Vincke, Preference Modelling, Springer, Berlin, 1985.

B. Roy, Un algorithme de classements fond$e sur le une repr$esentation Ooue des preferences en pr$esence de criteres multiples (la methode ELECTRE), Revue Francaise d’Informatique et de Recherche Operationnelle 8 (1968) 57–75.

B. Roy, Decision aid and decision making, European J. Oper. Res. 45 (1990) 324–331.

E. Szpilrajn, Sur l’extension de l’ordre partiel, Fund.Math. 16 (1930) 386–389.

W.T. Trotter, Combinatorics and Partially Ordered Sets.Dimension Theory, The Johns Hopkins University Press,

Baltimore and London, 1992.

M. Yannakakis, On the complexity ofthe partial order dimension problem, SIAM J. Algebra Discrete Math. 3 (1982)


J. Yañez, J. Montero, A poset dimension algorithm, J. Algorithms 30 (1999) 185–208.

L.A. Zadeh, Similarity relations and fuzzy orderings, Inform. Sci. 3 (1971) 177–200.

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