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The modes of convergence in the approximation of fuzzy random optimization problems

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Abstract

To develop the approximation approach to fuzzy random optimization problems, it is required to introduce the modes of convergence in fuzzy random theory. For this purpose, this paper first presents several novel convergence concepts for sequences of fuzzy random variables, such as convergence in chance, convergence in distribution and convergence in optimistic value; then deals with the convergence criteria and convergence relations among various types of convergence. Finally, we deal with the convergence theorems for sequences of integrable fuzzy random variables, including dominated convergence theorem and bounded convergence theorem.

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Authors and Affiliations

  1. College of Mathematics & Computer Science, Hebei University, 071002, Baoding, Hebei, China

    Yan-Kui Liu

  2. School of Creative Media, City University of Hong Kong, Hong Kong, China

    Zhi-Qiang Liu

  3. School of Information, Renmin University of China, 100872, Beijing, China

    Jinwu Gao

Authors
  1. Yan-Kui Liu
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  2. Zhi-Qiang Liu
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  3. Jinwu Gao
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Corresponding author

Correspondence to Yan-Kui Liu.

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Liu, YK., Liu, ZQ. & Gao, J. The modes of convergence in the approximation of fuzzy random optimization problems. Soft Comput 13, 117–125 (2009). https://doi.org/10.1007/s00500-008-0309-9

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