A New Method for Exploiting Fuzzy Preference Relations in Decision Agents

Eduardo Fernández González ¹ y Rafael Olmedo Pérez²

¹ Escuela de Informática Universidad Autónoma de Sinaloa; México eddyf@uas.uasnet.mx

² Facultad de Ciencias Físico Matemáticas Universidad Autónoma de Sinaloa; México, rolmedo@uas.uasnet.mx

Artículo recibido en abril 23, 2004 ]]> Aceptado en julio 30, 2004

Resumen

El enfoque normativo de la decisión ha predominado en la concepción de agentes inteligentes capaces de resolver problemas de selección de alternativas. En el trabajo se discuten las limitaciones de este paradigma y se sustenta otro basado en relaciones de preferencia borrosas, cuyo defecto fundamental radica en el momento de explotar la relación de preferencia para llegar a una prescripción. Se propone un nuevo método de explotación basado en la solución de un problema de optimización multiobjetivo que se resuelve en dos pasos, empleando en uno de ellos un algoritmo evolutivo. La propuesta posee mejores propiedades que otros procedimientos anteriores inspirados en ideas similares, pues logra modelar mejor y más sencillamente las preferencias sobre los atributos en conflicto.

Palabras Clave: Agente de decisión, Relación de preferencia borrosa, Prescripción, Optimización multiobjetivo, Algoritmo evolutivo.

Abstract

The normative approach for decision–making is the dominant paradigm in designing intelligent decision agents. We discuss here the advantages of a more flexible way based on fuzzy logic. However, most exploitation methods of fuzzy preference relations do not provide good prescriptions. Recently some approaches based on the idea of reducing inconsistencies using evolutionary multiobjective optimization have been proposed. In this work a new method is presented based on similar ideas but improving them. The multiobjective optimization problem is separated into two steps and solved with a better model of preferences, also using a simpler evolutionary algorithm. These improvements allow us to achieve better solutions in a simpler way than the previous methods.

Keywords: Decision agent, fuzzy preference relation, prescription, multiobjective optimization, evolutionary algorithm.

Referencias

1. Arrow, K.J., Raynaud, H. (1986): Social choice and multicriterion decision making, MIT Press, Cambridge.        [ Links ]

2. Bouyssou, D., Vincke, Ph. (1995): Ranking alternatives on the basis of preference relations: a progress report with special emphasis on outranking relations, Série Mathématiques de la Gestion, Université Libre de Bruxelles.        [ Links ]

3. Brans, J. P., Vincke Ph. (1985): A preference ranking organization method, Management Science 31, 647–656.        [ Links ]

4. Coello, C. (1999): A comprehensive survey of evolutionary–based multiobjective optimization techniques, Knowledge and Information Systems 1, 269–308.        [ Links ]

5. D'Avignon, G.R., Vincke, Ph. (1988): An outranking method under uncertainty, European Journal of Operational Research 36, 311–321.        [ Links ]

6. Fernández, E. Leyva, J.C (2002): Un método para resolver problemas de decisión a partir de una modelación flexible de preferencias basada en lógica borrosa, Computación y Sistemas 5, no. 4, 277–287.        [ Links ]

7. Fodor J., Roubens, M. (1994): Fuzzy Preference Modeling and Multicriteria Decision Support, Kluwer, Dordrecht.        [ Links ]

8. French, S. (1986): Decision Theory: an introduction to the mathematics of rationality, Halsted Press, NY– Brisbane–Chichester.        [ Links ]

9. Hokkanen, J., Salminen, P., 1997. Choosing a solid waste management system using multi criteria decision analysis. European Journal of Operational Research 98, no. 1, 19–36.        [ Links ]

10. Howard, R.A. y Matheson, J.E. (1984) (eds.): Readings on the principles and applications of Decision Analysis, Strategic Decisions Group, Menlo Park, California.        [ Links ]

11. Kahneman, D., Tversky, A. (2000): Choices, values and frames, Cambridge University Press, New York.        [ Links ]

12. Keeney, R.L., Raiffa, H. (1976): Decisions with multiple objectives. Preferences and value trade–offs, Wiley, New York.        [ Links ]

13. Leyva, J.C., Fernández, E. (1999): A genetic algorithm for deriving final ranking from a fuzzy outranking relation, Foundations of Computing and Decision Sciences 24, no. 1, 33–47.        [ Links ]

14. Leyva, J.C., Fernández, E. (2003): A new method for group decision support based on ELECTRE III methodology, European Journal of Operational Research 148, no. 1, 14–27.        [ Links ]

15. Leyva, J.C. (2000): Aplicación de los algoritmos genéticos a la solución del Problema de Decisión Multicriterio individual y en grupo", (resumen de tesis doctoral), Computación y Sistemas 4, no. 2, 178–188.        [ Links ]

16. Macharis C., Brans J.P., and Mareschal B. (1998): The GDSS PROMETHEE Procedure, Journal of Decision Systems 7, 283–307.        [ Links ]

17. Martel, J.M. , D'Avignon, G.R. (1982): Projects ordering with multicriteria analysis, European Journal of Operational Research 10, no. 1, 56–69.        [ Links ]

18. Michalewicz, Z. (1996): Genetic Algorithms + Data Structures = Evolution Programs, Springer Verlag, Berlin–Heidelberg–New York.        [ Links ]

19. Mousseau, V. (1995): Eliciting information concerning the relative importance of criteria, En: Pardalos, P., Siskos, Y. y Zopounidis, C., (eds) Advances in Multicriteria Analysis, Kluwer Academic Publishers, Dordrecht/Boston/London.        [ Links ]

20. Mousseau, V, Dias, L.C. (2004): Valued outranking relations in ELECTRE providing manageable disaggregation procedures, European Journal of Operational Research 156, no.2, 448–467.        [ Links ]

21. Orlovski, S.A. (1978): Decision–making with a fuzzy preference relation, Fuzzy Sets and Systems 1, 155–167.        [ Links ]

22. Perny, P., Roy, B. (1992): The use of fuzzy outranking relations in preference modeling, Fuzzy Sets and Systems 49, 33–53.        [ Links ]

23. Pomerol, Ch. (1995): Artificial Intelligence and Human Decision Making, En: Slowinski, R., (ed.) OR: Toward Intelligent Decision Support, 14^th European Conference on Operational Research, 169–196.        [ Links ]

24. Poon P.W., Carter J.N. (1995): Genetic algorithm crossover operators for ordering applications, Computers & Operations Research 22 , no. 1, 135–147.        [ Links ]

25. Rogers, M., Bruen, M., Maystre, L., 2000. ELECTRE and Decision Support, Kluwer, Boston–Dordrecht–London.        [ Links ]

26. Roy B., 1990. The outranking approach and the foundations of ELECTRE methods. En: Bana e Costa, C.A., (ed.) Reading in multiple criteria decision aid. Springer–Verlag, Berlin, 155–183.        [ Links ]

27. Roy, B. (1996): Multicriteria methodology for Decision Aiding, Kluwer Academic Publisher, Dordrecht– Boston– London.        [ Links ]

28. Roy B., and Vanderpooten D. (1995): The European School of MCDA: A Historical Review En: Slowinski, R. (ed.) OR: Toward Intelligent Decision Support, 14th European Conference on Operational Research, 39–65.        [ Links ]

29. Russell, S., Norvig, P. (1996): Inteligencia Artificial. Un enfoque moderno, Prentice Hall Hispanoamericana, México – Nueva York.        [ Links ]

30. Siskos, Y. (1983): Analyse de systemes de decision multicritere en univers aleatoire, Foundations of Control Engineering 8, 193–212.        [ Links ]

31. Zopounidis, C., Dimitras, A. (1998): Multicriteria Decision Aid methods for the prediction of business failure, Kluwer Academic Publishers, Boston/Dordrecht/London.        [ Links ]

Nota

¹ Esta investigación cuenta con el apoyo de CONACYT.