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

Deguo Yang (), Zhaojun Zong () and Feng Hu ()
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Deguo Yang: Qufu Normal University
Zhaojun Zong: Qufu Normal University
Feng Hu: Qufu Normal University

Fuzzy Optimization and Decision Making, 2025, vol. 24, issue 3, No 6, 485-529

Abstract: 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.

Keywords: Continuity; Convergence; Uncertain random sequence; U-S chance space (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10700-025-09454-0

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