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Abstract

CPTS-integrals (Cumulative Prospect Theory Sugeno integral) are agregation functions that return a global rating when the evaluations are given on a bipolar scale. This paper presents the problem of the elicitation of CPTS-integrals agreeing with a data set composed of pairs concerning some criteria and a global evaluation. Moreover the set of fuzzy measures which are solutions of this inverse problem is identified. When the elicitation of one CPTS-integral is not possible, a set of family of CPTS-integrals is proposed.

Keywords

S-integral CPTS-integral fuzzy measures bipolar scale 

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References

  1. 1.
    Pap, E., Mihailović, B.P.: A representation of a comonotone-\(\textcircled{V}\)-additive and monotone functional by two Sugeno integrals. Fuzzy Sets and Systems 155, 77–88 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Rico, A., Grabisch, M., Labreuche, C., Chateauneuf, A.: Preference modelling on totally ordered sets by the Sugeno integral. Discrete Applied Mathematics 147, 113–124 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Prade, H., Rico, A., Serrurier, M., Raufaste, E.: Elicitating Sugeno Integrals: Methodology and a Case Study. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS, vol. 5590, pp. 712–723. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Sugeno, M.: Ordinal Preference Models Based on S-Integrals and Their Verification. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L., et al. (eds.) Nonlinear Mathematics for Uncertainty and its Applications. AISC, vol. 100, pp. 1–18. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Sugeno, M.: Theory of fuzzy integrals and its applications, Ph.D. Thesis, Tokyo Institute of Technology (1974)Google Scholar
  6. 6.
    Grabisch, M., Labreuche, C.: A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. Annals OR 175(1), 247–286 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Dubois, D., Prade, H.: Bipolar Representations in Reasoning, Knowledge Extraction and Decision Processes. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 15–26. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Grabisch, M.: The symmetric Sugeno integral. Fuzzy Sets and Systems 139, 473–490 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Marichal, J.-L.: Weighted lattice polynomials. Discrete Mathematics 309, 814–820 (2009)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Agnès Rico
    • 1
  • Michio Sugeno
    • 2
  1. 1.ERICUniversité de LyonLyonFrance
  2. 2.European Centre for Soft ComputingMieres-AsturiasSpain

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