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A Quantile Approach to Integration with Respect to Non-additive Measures

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Modeling Decisions for Artificial Intelligence (MDAI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7647))

Abstract

The aim of this paper is to introduce some classes of aggregation functionals when the evaluation scale is a complete lattice.

We focus on the notion of quantile of a lattice-valued function which have several properties of its real-valued counterpart and we study a class of aggregation functionals that generalizes Sugeno integrals to the setting of complete lattices. Then we introduce in the real-valued case some classes of aggregation functionals that extend Choquet and Sugeno integrals by considering a multiple quantile model generalizing the approach proposed in [3].

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Author information

Authors and Affiliations

  1. Department of Economics, University Cà Foscari of Venice, Cannaregio 873, 30121, Venice, Italy

    Marta Cardin

Authors
  1. Marta Cardin
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Editor information

Editors and Affiliations

  1. IIIA-CSIC, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

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

    Yasuo Narukawa

  3. Universitat de Girona, Campus Montilivi, building EPS-4, 17071, Girona, Spain

    Beatriz López  & Mateu Villaret  & 

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Cardin, M. (2012). A Quantile Approach to Integration with Respect to Non-additive Measures. In: Torra, V., Narukawa, Y., López, B., Villaret, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2012. Lecture Notes in Computer Science(), vol 7647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34620-0_14

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  • DOI: https://doi.org/10.1007/978-3-642-34620-0_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34619-4

  • Online ISBN: 978-3-642-34620-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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