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Continuity of Choquet Integrals of Supermodular Capacities

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Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods (IPMU 2010)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 80))

Abstract

We prove the continuity of the Choquet integral of supermodular capacities, in L  ∞  with respect to the weak*-topology, employing a useful relationship between convex games and their Choquet integrals. The main result is applied to generalized fair division problems, and the existence of Pareto optimal α-allocations is demonstrated for the case of nonadditive measures.

MSC 2000: Primary: 28B05, 28E10; secondary: 91A12.

This research is supported by a Grant-in-Aid for Scientific Research (No. 21530277) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.

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Author information

Authors and Affiliations

  1. Faculty of Economics, Hosei University, 4342, Aihara, Machida, Tokyo, 194–0298, Japan

    Nobusumi Sagara

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  1. Nobusumi Sagara
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Editors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany

    Eyke Hüllermeier

  2. Department of Knowledge Processing and Language Engineering, Otto-von-Guericke University of Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Rudolf Kruse

  3. Fakultät für Elektrotechnik und Informationstechnik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Frank Hoffmann

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Sagara, N. (2010). Continuity of Choquet Integrals of Supermodular Capacities. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. IPMU 2010. Communications in Computer and Information Science, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14055-6_49

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  • DOI: https://doi.org/10.1007/978-3-642-14055-6_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14054-9

  • Online ISBN: 978-3-642-14055-6

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