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Choquet integral with respect to a symmetric fuzzy measure of a function on the real line

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Abstract

Some results about the calculation of the Choquet integral of a monotone function are presented. The construction of monotone functions from non-monotone ones that lead to the same Choquet integral is studied.

The paper is completed with the application of these results to the continuous WOWA operator, as well as with some differential equations also applied to the determination of the weight in this operator.

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Author information

Authors and Affiliations

  1. Toho Gakuen, 3-1-10, Naka, Kunitachi, Tokyo, 186-0004, Japan

    Yasuo Narukawa

  2. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259, Nagatuta, Midori-ku, Yokohama, 226-8502, Japan

    Yasuo Narukawa

  3. IIIA—CSIC, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  4. European Centre for Soft Computing, 33600, Mieres-Asturias, Spain

    Michio Sugeno

Authors
  1. Yasuo Narukawa
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  2. Vicenç Torra
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  3. Michio Sugeno
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Corresponding author

Correspondence to Yasuo Narukawa.

Additional information

Partial support by the Spanish MEC (projects ARES—CONSOLIDER INGENIO 2010 CSD2007-00004, eAEGIS—TSI2007-65406-C03-02 and Co-Privacy—TIN2011-27076-C03-03) is acknowledged.

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Narukawa, Y., Torra, V. & Sugeno, M. Choquet integral with respect to a symmetric fuzzy measure of a function on the real line. Ann Oper Res 244, 571–581 (2016). https://doi.org/10.1007/s10479-012-1166-6

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  • DOI: https://doi.org/10.1007/s10479-012-1166-6

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