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Learning Fuzzy-Valued Fuzzy Measures for the Fuzzy-Valued Sugeno Fuzzy Integral

  • Conference paper
Computational Intelligence for Knowledge-Based Systems Design (IPMU 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6178))

Abstract

Fuzzy integrals are very useful for fusing confidence or opinions from a variety of sources. These integrals are non-linear combinations of the support functions with the (possibly subjective) worth of subsets of the sources, realized by a fuzzy measure. There have been many applications and extensions of fuzzy integrals and this paper deals with a Sugeno integral where both the integrand and the measure take on fuzzy number values. A crucial aspect of using fuzzy integrals for fusion is determining or learning the measures. Here, we propose a genetic algorithm with novel cross-over and mutation operators to learn fuzzy-valued fuzzy measures for a fuzzy-valued Sugeno integral.

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References

  1. Grabisch, M., Nguyen, H., Walker, E.: Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference. Kluwer Academic Publishers, London (1994)

    MATH  Google Scholar 

  2. Grabisch, M., Murofushi, T., Sugeno, M. (eds.): Fuzzy Measures and Integrals: Theory and Applications. Physica-Verlag, Heidelberg (2000)

    MATH  Google Scholar 

  3. Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall, New Jersey (1995)

    MATH  Google Scholar 

  4. Auephanwiriyakul, S., Keller, J., Gader, P.: Generalized Choquet Fuzzy Integral Fusion. Information Fusion 3, 69–85 (2002)

    Article  Google Scholar 

  5. Guo, C., Zhang, D., Wu, C.: Fuzzy-valued measures and generalized fuzzy integrals. Fuzzy Sets and Systems 97, 255–260 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  6. Wu, C., Wang, S., Ma, M.: Generalized fuzzy integrals I. Fuzzy Sets and Systems 57, 219–226 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  7. Wu, C., Wang, S., Ma, M.: Generalized fuzzy integrals II. Fuzzy Sets and Systems 70, 75–87 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  8. Zhang, D., Wang, Z.: Fuzzy integrals of fuzzy-valued functions. Fuzzy Sets and Systems 54, 63–67 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  9. Zhang, D., Guo, C.: Generalized fuzzy integrals of set-valued functions. Fuzzy Sets and Systems 76, 365–373 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Bezdek, J.C., Keller, J.M., Krishnapuram, R., Pal, N.R.: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Kluwer, Norwell (1999)

    MATH  Google Scholar 

  11. Engelbrecht, A.: Computational Intelligence: An Introduction, 2nd edn. John Wiley, Chichester (2007)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Electrical and Computer Engineering Department, University of Missouri, Columbia, MO, 65211, USA

    Derek T. Anderson, James M. Keller & Timothy C. Havens

Authors
  1. Derek T. Anderson
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  2. James M. Keller
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  3. Timothy C. Havens
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Str., 35032, Marburg, Germany

    Eyke Hüllermeier

  2. Fakultät Informatik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Rudolf Kruse

  3. Fakultät für Elektrotechnik und Informationstechnik, Technische Universität Dortmund, Otto-Hahn-Str. 4, 44227, Dortmund, Germany

    Frank Hoffmann

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© 2010 Springer-Verlag Berlin Heidelberg

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Anderson, D.T., Keller, J.M., Havens, T.C. (2010). Learning Fuzzy-Valued Fuzzy Measures for the Fuzzy-Valued Sugeno Fuzzy Integral. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Computational Intelligence for Knowledge-Based Systems Design. IPMU 2010. Lecture Notes in Computer Science(), vol 6178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14049-5_52

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  • DOI: https://doi.org/10.1007/978-3-642-14049-5_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14048-8

  • Online ISBN: 978-3-642-14049-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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