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The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space

Author

Listed:
  • Li Guan

    (Faculty of Science, College of Statistics and Data Science, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, China)

  • Juan Wei

    (Faculty of Science, College of Statistics and Data Science, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, China)

  • Hui Min

    (Faculty of Science, College of Statistics and Data Science, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, China)

  • Junfei Zhang

    (School of Statistics and Mathematics, Central University of Finance and Economics, 39 South College Road, Haidian District, Beijing 100081, China)

Abstract

In this paper, we firstly introduce the definition of the fuzzy metric of sets, and discuss the properties of fuzzy metric induced by the Hausdorff metric. Then we prove the limit theorems for set-valued random variables in fuzzy metric space; the convergence is about fuzzy metric induced by the Hausdorff metric. The work is an extension from the classical results for set-valued random variables to fuzzy metric space.

Suggested Citation

  • Li Guan & Juan Wei & Hui Min & Junfei Zhang, 2021. "The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space," Mathematics, MDPI, vol. 9(11), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1192-:d:561596
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    References listed on IDEAS

    as
    1. Robert Lee Taylor & Ronald Frank Patterson, 1985. "Strong laws of large numbers for arrays of row-wise exchangeable random elements," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 8, pages 1-10, January.
    2. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
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