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On the Interpretation of Some Fuzzy Integrals

  • Vicenç Torra
  • Yasuo Narukawa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3131)

Abstract

In this work we study the interpretation of some fuzzy integrals (Choquet, Sugeno and twofold integrals). We give some examples of their use and from them we study the meaning and interest of the integral. We show that fuzzy inference systems, for both disjunctive and conjunctive rules, can be interpreted in terms of Sugeno integrals. This permits to consider a new field for the application of Sugeno integrals.

Keywords

Fuzzy integrals Sugeno integral Fuzzy inference system Twofold integral 

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References

  1. 1.
    Benvenuti, P., Mesiar, R., Vivona, D.: Monotone Set Functions-Based Integrals. In: Pap, E. (ed.) Handbook of Measure Theory, Elsevier, Amsterdam (2002)Google Scholar
  2. 2.
    Calvo, T., Mayor, G., Mesiar, R.: Aggregation Operators. Physica-Verlag (2002)Google Scholar
  3. 3.
    Calvo, T., Mesiarová, A., Valásková, L.: Composition of aggregation operators - one more new construction method, In: Proc. Agop, Alcala, pp.51-53 (2003)Google Scholar
  4. 4.
    Choquet, G.: Theory of Capacities. Ann. Inst. Fourier 5, 131–296 (1954)MathSciNetGoogle Scholar
  5. 5.
    Dubois, D., Prade, H.: Weighted minimum and maximum operations. Information Sciences 39, 205–210 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall, U.K (1995)Google Scholar
  7. 7.
    Murofushi, T., Sugeno, M.: Fuzzy t-conorm integral with respect to fuzzy measures: generalization of Sugeno integral and Choquet integral. Fuzzy Sets and Systems 42(1), 57–71 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Murofushi, T., Sugeno, M.: Fuzzy Measures and Fuzzy Integrals. In: Grabisch, M., Murofushi, T., Sugeno, M. (eds.) Fuzzy Measures and Integrals: Theory and Applications, pp. 3–41. Physica-Verlag, Heidelberg (2000)Google Scholar
  9. 9.
    Narukawa, Y., Torra, V.: Twofold integral: a graphical interpretation and its generalization to universal sets. In: Proc. EUSFLAT 2003, Zittau, Germany, pp. 718–722 (2003)Google Scholar
  10. 10.
    Narukawa, Y., Torra, V.: Twofold integral and Multi-step Choquet integral. Kybernetika 40, 39–50 (2004)MathSciNetGoogle Scholar
  11. 11.
    Sugeno, M.: Theory of fuzzy integrals and its application, Doctoral Thesis . Tokyo Institute of Technology (1974)Google Scholar
  12. 12.
    Takahagi, E.: On fuzzy integral representation in fuzzy switching functions, fuzzy rules and fuzzy control rules. In: IFSA, Prof. 8th IFSAWorld Congres, pp. 289–293 (1999)Google Scholar
  13. 13.
    Torra, V.: Twofold integral: A Choquet integral and Sugeno integral generalization, Butllet´ı de l’Associació Catalana d’Intel·ligència Artificial, 29 13-19 (in Catalan). Preliminary version: IIIA Research Report TR-2003-08, in English (2003)Google Scholar
  14. 14.
    Yoneda, M., Fukami, S., Grabisch, M.,, M.: Human factor and fuzzy science. In: Asai, K. (ed.) Fuzzy science, Kaibundo, pp. 93–122 (1994) (in Japanese)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Vicenç Torra
    • 1
  • Yasuo Narukawa
    • 2
  1. 1.Institut d’Investigació en Intel·ligència ArtificialBellaterraSpain
  2. 2.Toho GakuenTokyoJapan

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