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On Convergence Theorems of Set-Valued Choquet Integrals

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Nonlinear Mathematics for Uncertainty and its Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

Abstract

The article aims at discussing the Choquet integrals of set-valued random variables with respect to capacities. We firstly state representation theorems and subadditive property of set-valued Choquet integrals. Then we mainly prove Fatou’s Lemmas, Lesbesgue dominated convergence theorem and monotone convergence theorems of set-valued Choquet integrals under the weaker conditions than that in previous works.

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Authors and Affiliations

  1. Department of Applied Mathematics, Beijing University of Technology, Beijing, 100124, P.R. China

    Hongxia Wang & Shoumei Li

Authors
  1. Hongxia Wang
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  2. Shoumei Li
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Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

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Wang, H., Li, S. (2011). On Convergence Theorems of Set-Valued Choquet Integrals. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_12

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

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