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On convergences of uncertain random sequences under U-S chance spaces

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Listed:
  • Deguo Yang

    (Qufu Normal University)

  • Zhaojun Zong

    (Qufu Normal University)

  • Feng Hu

    (Qufu Normal University)

Abstract

Convergence has been a topic of considerable interest. This study further develops U-S chance theory to investigate convergences for uncertain random sequences in complex systems where human uncertainty and randomness with sub-linear characteristics coexist. Building upon two existing chance measures, this paper defines two new chance measures, presents their properties and proves the relationship among the four chance measures. Six expectations of uncertain random variables under U-S chance spaces are suggested based on Choquet integrals and sub-linear expectations. Meanwhile, their relationship and Markov’s inequality are proven. Furthermore, this paper systematically presents multiple definitions of the continuities for chance measures under U-S chance spaces and investigate the relationships among them. Based on the continuity assumption of uncertain measure, a new version of Borel-Cantelli lemma under U-S chance spaces is proven. Finally, several definitions of convergences for uncertain random sequences under U-S chance spaces are presented. By rigorous mathematical proofs and systematic construction of counterexamples, the relationships among different types of convergences are illustrated.

Suggested Citation

  • Deguo Yang & Zhaojun Zong & Feng Hu, 2025. "On convergences of uncertain random sequences under U-S chance spaces," Fuzzy Optimization and Decision Making, Springer, vol. 24(3), pages 485-529, September.
    • Handle: RePEc:spr:fuzodm:v:24:y:2025:i:3:d:10.1007_s10700-025-09454-0
    DOI: 10.1007/s10700-025-09454-0
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    References listed on IDEAS

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    1. Chen, Zengjing & Epstein, Larry G. & Zhang, Guodong, 2023. "A central limit theorem, loss aversion and multi-armed bandits," Journal of Economic Theory, Elsevier, vol. 209(C).
    2. Feng Hu & Ziyi Qu & Deguo Yang, 2025. "Uncertain random programming models in the framework of U-S chance theory and their applications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(1), pages 161-194, April.
    3. H. Ahmadzade & Y. Sheng & M. Esfahani, 2017. "On the convergence of uncertain random sequences," Fuzzy Optimization and Decision Making, Springer, vol. 16(2), pages 205-220, June.
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