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Exploitation of a Rough Approximation of the Outranking Relation in Multicriteria Choice and Ranking

  • Salvatore Greco
  • Benedetto Matarazzo
  • Roman Slowinski
  • Alexis Tsoukiàs
Chapter
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 465)

Abstract

Given a finite set A of actions evaluated by a family of criteria, we consider a preferential information in the form of a pairwise comparison table (PCT) including pairs of actions from a subset B⊆AxA described by graded preference relations on particular criteria and a comprehensive outranking relation. Using the rough set approach to the analysis of the PCT, we obtain a rough approximation of the outranking relation by a graded dominance relation. Decision rules derived from this approximation are then applied to a set M⊆A of potential actions. As a result, we obtain a four-valued outranking relation on set M. The construction of a suitable exploitation procedure in order to obtain a recommendation for multicriteria choice and ranking is an open problem within this context. We propose an exploitation procedure that it is the only one satisfying some desirable properties.

Keywords

Rough sets multicriteria decision making four-valued outranking exploitation procedures 

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References

  1. Bouyssou, D., "Ranking methods based on valued preference relations: a characterization of the net-flow method", European Journal of Operational Research, 60,1992a, 61–68.CrossRefGoogle Scholar
  2. Bouyssou, D., "A note on the sum of differences choice function for fuzzy preference relations", Fuzzy sets and Systems, 47,1992b, 197–202.CrossRefGoogle Scholar
  3. Bouyssou, D., "Outranking Relations: Do they have special properties?", Journal of Multi-Criteria Decision Analysis 5 (2), 1996, 99–111.CrossRefGoogle Scholar
  4. Fishburn, P. C., The Theory of Social Choice, Princeton University Press, Princeton, NJ, 1973.Google Scholar
  5. Goodman, L. A., "On methods of amalgamation", in: R.M. Thrall, C.H. Coombs andRX. Davis, Eds., Decision Processes, Wiley, New York, 1954, 39–48.Google Scholar
  6. Greco S., Matarazzo, B., Slowinski, R.Rough Set Approach to Multi-Attribute Choice and Ranking Problems, ICS Research Report 38/95, Warsaw University of Technology, Warsaw, 1995. Also in: G. Fandel and T. Gal (Eds.), Multiple Criteria Decision Making, Springer-Verlag, Berlin, 1997, 318–329.CrossRefGoogle Scholar
  7. Greco S., Matarazzo, B., Slowinski, R., Rough Approximation of Preference Relation by Dominance Relations, ICS Research Report 16/96, Warsaw University of Technology, Warsaw, 1996. Also in: European Journal of Operational Research, to appear.Google Scholar
  8. Greco S., Matarazzo, B., Slowinski, R., Tsoukias, A., Exploitation of a rough approximation of the outranking relation, Cahier du LAMSADE, no. 152, University of Paris-Dauphine, Paris, 1997.Google Scholar
  9. Luce, R.D., "Semi-orders and a theory of utility discrimination", Econometrica 24, 1956, 178–191.CrossRefGoogle Scholar
  10. Henriet, D., "The Copeland choice function - An axiomatic characterization", Social Choice and Welfare, 2, 1985, 49–64.CrossRefGoogle Scholar
  11. Roy, B, Méthodolgie multicritère d’aide à la décision, Economica, Paris, 1985.Google Scholar
  12. Roy, B., "The outranking approach and the foundations of ELECTRE methods", Theory and Decision 31, 1991, 49–73.CrossRefGoogle Scholar
  13. Roy, B., "Decision science or decision aid science?", European Journal of Operational Research, Special Issue on Model Validation in Operations Research, 66,1993,184–203.Google Scholar
  14. Rubinstein, A., "Ranking the participants in a tournament", SIAM Journal of Applied Mathematics 38, 1980, 108–111.CrossRefGoogle Scholar
  15. Slowinski, R., Vanderpooten, D,, Similarity relation as a basis for rough approximations, ICS Research Report 53/95, Warsaw University of Technology, Warsaw, 1995.Google Scholar
  16. Slowinski, R., Vanderpooten, D., A generalized definition of rough approximation, ICS Research Report 4/96, Warsaw University of Technology, Warsaw, 1996.Google Scholar
  17. Slowinski, R., Vanderpooten, D., "A generalized definition of rough approximation based on similarity", to appear in IEEE Transactions on Data and Knowledge Engineering, 1998.Google Scholar
  18. Tsoukias, A., Vincke, Ph., "A new axiomatic foundation of the partial comparability theory", Theory and Decision, 39, 1995, 79–114.CrossRefGoogle Scholar
  19. Tsoukias, A., Vincke, Ph., "A new axiomatic foundation of partial comparability", in: J. Climaco (Ed.): Multicriteria Analysis, Springer-Verlag, Berlin, 1997, 37–50.CrossRefGoogle Scholar
  20. Tversky, A., "Features of similarity", Psychological Review, 84 (4), 1977, 327–352CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Salvatore Greco
    • 1
  • Benedetto Matarazzo
    • 1
  • Roman Slowinski
    • 2
  • Alexis Tsoukiàs
    • 3
  1. 1.University of CataniaCataniaItaly
  2. 2.Institute of Computing SciencePoznan University of TechnologyPoland
  3. 3.LAMSADEUniversité de Paris DauphineParis Cedex 16France

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