Choice Procedures in Pairwise Comparison Multiple-Attribute Decision Making Methods

  • Raymond Bisdorff
  • Marc Roubens
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3051)


We consider extensions of some classical rational axioms introduced in conventional choice theory to valued preference relations. The concept of kernel is revisited using two ways : one proposes to determine kernels with a degree of qualification and the other presents a fuzzy kernel where every element of the support belongs to the rational choice set with a membership degree. Links between the two approaches is emphasized. We exploit these results in Multiple-attribute Decision Aid to determine the good and bad choices. All the results are valid if the valued preference relations are evaluated on a finite ordinal scale.


Rational Choice Choice Procedure Boolean Matrix Fuzzy Relational Preference Comparison Decision 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bisdorff, R., Roubens, M.: On defining and computing fuzzy kernels from Lvalued simple graphs. In: Ruan, D., et al. (eds.) Intelligent Systems and Soft Computing for Nuclear science and Industry, FLINS 1996 Workshop, pp. 113–123. World Scientific Publishers, Singapore (1996)Google Scholar
  2. 2.
    Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multi-criteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)Google Scholar
  3. 3.
    Fodor, J.C., Perny, P., Roubens, M.: Decision Making and Optimization. In: Ruspini, E., Bonissone, P., Pedrycz, W. (eds.) Handbook of Fuzzy Computation, pp.F.5.1 : 1–14. Institute of Physics Publications/Oxford University Press, Bristol (1998)Google Scholar
  4. 4.
    Fodor, J., Orlovski, S.A., Perny, P., Roubens, M.: The use of fuzzy preference models in multiple criteria: choice, ranking and sorting. In: Dubois, D., Prade, H. (eds.) Handbooks and of Fuzzy Sets. Operations Research and Statistics, vol. 5, pp. 69–101. Kluwer Academic Publishers, Dordrecht (1998)Google Scholar
  5. 5.
    Kitainik, L.: Fuzzy Decision Procedures with Binary Relations: towards an unified Theory. Kluwer Academic Publishers, Dordrecht (1993)zbMATHGoogle Scholar
  6. 6.
    Marichal, J.-L.: Aggregation of interacting criteria by means of the discrete Choquet integral. In: Calvo, T., Mayor, G., Mesiar, R. (eds.) Aggregation operators: new trends and applications. Studies in Fuzziness and Soft Computing, vol. 97, pp. 224–244. Physica-Verlag, Heidelberg (2002)Google Scholar
  7. 7.
    Perny, P., Roubens, M.: Fuzzy Relational Preference Modelling. In: Dubois, D., Prade, H. (eds.) Handbooks of Fuzzy Sets. Operations Research and Statistics, vol. 5, pp. 3–30. Kluwer Academic Publishers, Dordrecht (1998)Google Scholar
  8. 8.
    Roy, B.: Algèbre moderne et théorie des graphes, p. 2. Dunod, Paris (1969)zbMATHGoogle Scholar
  9. 9.
    Schmidt, G., Str Ühlein, T.: Relations and Graphs; Discrete mathematics for Computer Scientists. Springer, Heidelberg (1991)Google Scholar
  10. 10.
    Schwartz, T.: The logic of Collective Choice. Columbia Univer Press, New York (1986)Google Scholar
  11. 11.
    von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behaviour. Princeton University Press, New York (1953)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Raymond Bisdorff
    • 1
  • Marc Roubens
    • 2
  1. 1.Department of Management and InformaticsUniversity Center of Luxembourg 
  2. 2.Department of MathematicsUniversity of Liege 

Personalised recommendations