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A Lyapunov-Type Theorem for Nonadditive Vector Measures

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Modeling Decisions for Artificial Intelligence (MDAI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5861))

Abstract

We prove the convexity and compactness of the closure of the lower partition range of an ℝn-valued, nonatomic, supermodular capacity, employing a useful relationship between convex games and their Choquet integrals. The main result is applied to fair division problems, and the existence of Pareto optimal α-fair partitions is demonstrated for the case of nonadditive measures.

This research is supported by a Grant-in-Aid for Scientific Research (No. 18610003) 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

Authors
  1. Nobusumi Sagara
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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, Kunitachi, 186-0004, Tokyo, Japan

    Yasuo Narukawa

  3. Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, 560-8531, Osaka, Japan

    Masahiro Inuiguchi

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Sagara, N. (2009). A Lyapunov-Type Theorem for Nonadditive Vector Measures. In: Torra, V., Narukawa, Y., Inuiguchi, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2009. Lecture Notes in Computer Science(), vol 5861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04820-3_7

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  • DOI: https://doi.org/10.1007/978-3-642-04820-3_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04819-7

  • Online ISBN: 978-3-642-04820-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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