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An Algorithm for Identifying Fuzzy Measures with Ordinal Information

  • Pedro Miranda
  • Michel Grabisch
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 16)

Abstract

Consider a decision problem in which the preferences of the decision maker can be modelled through the Choquet integral [2] with respect to a fuzzy measure [10]. This means that he follows some behavioural rules while making decision (see [1], [9]). Next step consists in obtaining such a measure. The problem of identifying fuzzy measures from learning data has always been a difficult problem occurring in the practical use of fuzzy measures [5], [6].

Keywords

Decision Maker Numerical Scale Interval Scale Fuzzy Measure Quadratic Problem 
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.

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References

  1. 1.
    A. Chateauneuf. Comonotonic axioms and RDEU theory for arbitrary consequences. Journal of Mathematical Economics,to appear.Google Scholar
  2. 2.
    G. Choquet. Theory of capacities. Annales de l’Institut Fourier, (5): 131–295, 1953.MathSciNetCrossRefGoogle Scholar
  3. 3.
    C. A. Bana e Costa and J.-C. Vansnick. A theoretical framework for Measuring Attractiveness by a Categorical Based Evaluation TecHnique (MACBETH). In Jo ao Clímaco, editor, Multicriteria Analysis, pages 15–24. Springer, 1997.CrossRefGoogle Scholar
  4. 4.
    M. Grabisch. k-order additive discrete fuzzy measures. In Proceedings of 6th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU), pages 1345–1350, Granada (Spain), 1996.Google Scholar
  5. 5.
    M. Grabisch. Alternative representations of discrete fuzzy measures for decision making Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, 5: 587–607, 1997.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    M. Grabisch and J.-M. Nicolas. Classification by fuzzy integral-performance and tests. Fuzzy Sets and Systems, Special Issue on Pattern Recognition, (65): 255–271, 1994.MathSciNetCrossRefGoogle Scholar
  7. 7.
    P. Miranda and M. Grabisch. Optimization issues for fuzzy measures. International Journal of uncertainty, Fuzziness and Knowledge-Based Systems, 7 (6): 545–560, 1999.MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    G. C. Rota. On the foundations of combinatorial theory I. Theory of Möbius functions. Zeitschrift fur Wahrscheinlichkeitstheorie and Verwandte Gebeite, (2): 340–368, 1964.MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    D. Schmeidler. Integral representation without additivity. Proc. of the Amer. Math. Soc., (97(2)): 255–261, 1986.MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    M. Sugeno. Theory of fuzzy integrals and its applications. PhD thesis, Tokyo Institute of Technology, 1974.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Pedro Miranda
    • 1
  • Michel Grabisch
    • 2
  1. 1.Departamento de EstadísticaI.O. y D.M.OviedoSpain
  2. 2.Université Pierre et Marie Curie- LIP6ParisFrance

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