Searching for the dimension of valued preference relations

International Journal of Approximate Reasoning

Volumn 33, Issue 2, 2003, Pages 133-157

  Gonzalez Pachon J ^a   Gomez D ^b   Montero, J ^b   Yanez J ^b  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Dimension theory; Multicriteria decision analysis; Valued relations

Indexed keywords

DECISION MAKING; MATHEMATICAL OPERATORS; PROBLEM SOLVING; THEOREM PROVING;

VALUED RELATIONS;

INFORMATION ANALYSIS;

EID: 0037650964     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0888-613X(02)00150-0     Document Type: Article

References (25)

1. Adnadjevic D. Dimension of fuzzy ordered sets. Fuzzy Sets and Systems. 67:1994;349-357.
2. Belton V., Hodgkin J. Facilitators, decision makers, DIY users: Is intelligent multicriteria decision support for all feasible or desirable? European Journal of Operational Research. 113:1999;247-260.
3. Cutello V., Montero J. Fuzzy rationality measures. Fuzzy Sets and Systems. 62:1994;39-54.
4. Doignon J.P., Mitasm J. Dimension of valued relations. European Journal of Operational Research. 125:2000;571-587.
5. Dushnik B., Miller E.W. Partially ordered sets. American Journal of Mathematics. 63:1941;600-610.
6. Fodor J.C., Roubens M. Structure of valued binary relations. Mathematical Social Sciences. 30:1995;71-94.
7. J. González-Pachón, D. Gómez, J. Montero, J. Yáñez, Soft dimension theory, Fuzzy Sets and Systems, in press [ S0165-0114(02)00437-2].
8. González-Pachón J., Ríos-Insua S. A method for searching rationality in pairwise choices. Fandel G., Gal T. Multiple Criteria Decision Making. Lecture Notes in Economics and Mathematical Systems. vol. 448:1997;374-382 Springer.
9. González-Pachón J., Ríos-Insua S. Mixture of maximal quasi orders: a new approach to preference modelling. Theory and Decisions. 47:1999;73-88.
10. Macharis C., Brans J.P. The GDSS promethee procedure. Journal of Decision Systems. 7:1998;283-307.
11. Montero J. Arrow's theorem under fuzzy rationality. Behavioral Science. 32:1987;267-273.
12. J. Montero, J. Yáñez, 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.
13. J. Montero, J. Yáñez, D. Gómez, J. González-Pachón, Consistency in dimension theory, in: Proceedings of the Workshop on Preference Modelling and Applications, Granada, 2001, pp. 93-98.
14. Ovchinnikov S.V. Representation of transitive fuzzy relations. Skala H.J., Termini S., Trillas E. Aspects of Vagueness. 1984;105-118 Reidel, Amsterdam.
15. Pattanaik P.K. Voting and Collective Choice. 1971;Cambridge University Press, London.
16. Roy B. Decision aid and decision making. European Journal of Operational Research. 45:1990;324-331.
17. Sen A.K. Collective Choice and Social Welfare. 1970;Holden-Day, San Francisco.
18. Shafer G. Savage revisited (with discussion). Statistical Science. 1:1986;435-462.
19. Siskos Y., Spyridakos A. Intelligent multicriteria decision support: overview and perspectives. European Journal of Operational Research. 113:1999;236-246.
20. Szpilrajn E. Sur l'extension de l'ordre partiel. Fundamenta Mathematicae. 16:1930;386-389.
21. Trotter W.T. Combinatorics and Partially Ordered Sets. Dimension Theory. 1992;The Johns Hopkins University Press, Baltimore.
22. Valverde L. On the structure of F-indistinguishability operators. Fuzzy Sets and Systems. 17:1985;313-328.
23. Yannakakis M. On the complexity of the partial order dimension problem. SIAM Journal of Algebra and Discrete Mathematics. 3:1982;351-358.
24. Yáñez J., Montero J. A poset dimension algorithm. Journal of Algorithms. 30:1999;185-208.
25. Zadeh L.A. Similarity relations and fuzzy orderings. Informations Sciences. 3:1971;177-200.