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Derivative for Discrete Choquet Integrals

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Modeling Decisions for Artificial Intelligence (MDAI 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11676))

Abstract

In this paper we study necessary and sufficient conditions for the existence of the derivative for fuzzy measures when we are considering the Choquet integral. Results apply to discrete domains. The main result is based on the definition we introduce of compatible permutation for two pairs of measures \((\mu ,\nu )\).

As an application of the main result, we present the conditions for possibility measures.

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References

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Author information

Authors and Affiliations

  1. Tamagawa University, 6-1-1 Tamagawagakuen, Machida, Tokyo, 194-8610, Japan

    Yasuo Narukawa

  2. Hamilton Institute, Maynooth University, Eolas building, North Campus, Maynooth, Ireland

    Vicenç Torra

Authors
  1. Yasuo Narukawa
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  2. Vicenç Torra
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Corresponding author

Correspondence to Vicenç Torra .

Editor information

Editors and Affiliations

  1. Maynooth University, Maynooth, Ireland

    Vicenç Torra

  2. Tamagawa University, Machida, Tokyo, Japan

    Yasuo Narukawa

  3. University of Milano-Bicocca, Milan, Italy

    Gabriella Pasi

  4. University of Milano-Bicocca, Milan, Italy

    Marco Viviani

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Narukawa, Y., Torra, V. (2019). Derivative for Discrete Choquet Integrals. In: Torra, V., Narukawa, Y., Pasi, G., Viviani, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2019. Lecture Notes in Computer Science(), vol 11676. Springer, Cham. https://doi.org/10.1007/978-3-030-26773-5_13

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  • DOI: https://doi.org/10.1007/978-3-030-26773-5_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26772-8

  • Online ISBN: 978-3-030-26773-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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