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The Concave and Decomposition Integrals: A Review and Future Directions

AGOP Conference 2019 in Olomouc

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New Trends in Aggregation Theory (AGOP 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 981))

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Abstract

The concave and decomposition-integrals for capacities defined over finite spaces are introduced. The decomposition integral is based on allowable decompositions of a random variable and it generalizes the Choquet, concave, Shilkret and Pan integrals. Further research directions are given at the end of the paper.

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Notes

  1. 1.

    Coincidentally, the notation \(\mathcal{F}^{Ch}\), derived from the word chain, resonates with the notation \(\int ^{Ch}\) that derives from Choquet.

  2. 2.

    \(X \cdot \alpha _j\) denotes the inner product of X and \( \alpha _j\).

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel

    Ehud Lehrer

  2. INSEAD, Bd. de Constance, 77305, Fontainebleau Cedex, France

    Ehud Lehrer

Authors
  1. Ehud Lehrer
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Correspondence to Ehud Lehrer .

Editor information

Editors and Affiliations

  1. Faculty of Science, Palacký University, Olomouc, Czech Republic

    Radomír Halaš

  2. Systems Research Institute, Polish Academy of Science, Warsaw, Poland

    Marek Gagolewski

  3. Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

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Lehrer, E. (2019). The Concave and Decomposition Integrals: A Review and Future Directions. In: Halaš, R., Gagolewski, M., Mesiar, R. (eds) New Trends in Aggregation Theory. AGOP 2019. Advances in Intelligent Systems and Computing, vol 981. Springer, Cham. https://doi.org/10.1007/978-3-030-19494-9_2

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