Further results on laws of large numbers for uncertain random variables

Feng Hu; Xiaoting Fu; Ziyi Qu; Zhaojun Zong

Kybernetika (2023)

  • Volume: 59, Issue: 2, page 314-338
  • ISSN: 0023-5954

Abstract

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The uncertainty theory was founded by Baoding Liu to characterize uncertainty information represented by humans. Basing on uncertainty theory, Yuhan Liu created chance theory to describe the complex phenomenon, in which human uncertainty and random phenomenon coexist. In this paper, our aim is to derive some laws of large numbers (LLNs) for uncertain random variables. The first theorem proved the Etemadi type LLN for uncertain random variables being functions of pairwise independent and identically distributed random variables and uncertain variables without satisfying the conditions of regular, independent and identically distributed (IID). Two kinds of Marcinkiewicz-Zygmund type LLNs for uncertain random variables were established in the case of p ∈ ( 0 , 1 ) by the second theorem, and in the case of p > 1 by the third theorem, respectively. For better illustrating of LLNs for uncertain random variables, some examples were stated and explained. Compared with the existed theorems of LLNs for uncertain random variables, our theorems are the generalised results.

How to cite

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Hu, Feng, et al. "Further results on laws of large numbers for uncertain random variables." Kybernetika 59.2 (2023): 314-338. <http://eudml.org/doc/299096>.

@article{Hu2023,
abstract = {The uncertainty theory was founded by Baoding Liu to characterize uncertainty information represented by humans. Basing on uncertainty theory, Yuhan Liu created chance theory to describe the complex phenomenon, in which human uncertainty and random phenomenon coexist. In this paper, our aim is to derive some laws of large numbers (LLNs) for uncertain random variables. The first theorem proved the Etemadi type LLN for uncertain random variables being functions of pairwise independent and identically distributed random variables and uncertain variables without satisfying the conditions of regular, independent and identically distributed (IID). Two kinds of Marcinkiewicz-Zygmund type LLNs for uncertain random variables were established in the case of $p \in (0, 1)$ by the second theorem, and in the case of $p > 1$ by the third theorem, respectively. For better illustrating of LLNs for uncertain random variables, some examples were stated and explained. Compared with the existed theorems of LLNs for uncertain random variables, our theorems are the generalised results.},
author = {Hu, Feng, Fu, Xiaoting, Qu, Ziyi, Zong, Zhaojun},
journal = {Kybernetika},
keywords = {law of large numbers; uncertain random variable; Etemadi type theorem; Marcinkiewicz–Zygmund type theorem},
language = {eng},
number = {2},
pages = {314-338},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Further results on laws of large numbers for uncertain random variables},
url = {http://eudml.org/doc/299096},
volume = {59},
year = {2023},
}

TY - JOUR
AU - Hu, Feng
AU - Fu, Xiaoting
AU - Qu, Ziyi
AU - Zong, Zhaojun
TI - Further results on laws of large numbers for uncertain random variables
JO - Kybernetika
PY - 2023
PB - Institute of Information Theory and Automation AS CR
VL - 59
IS - 2
SP - 314
EP - 338
AB - The uncertainty theory was founded by Baoding Liu to characterize uncertainty information represented by humans. Basing on uncertainty theory, Yuhan Liu created chance theory to describe the complex phenomenon, in which human uncertainty and random phenomenon coexist. In this paper, our aim is to derive some laws of large numbers (LLNs) for uncertain random variables. The first theorem proved the Etemadi type LLN for uncertain random variables being functions of pairwise independent and identically distributed random variables and uncertain variables without satisfying the conditions of regular, independent and identically distributed (IID). Two kinds of Marcinkiewicz-Zygmund type LLNs for uncertain random variables were established in the case of $p \in (0, 1)$ by the second theorem, and in the case of $p > 1$ by the third theorem, respectively. For better illustrating of LLNs for uncertain random variables, some examples were stated and explained. Compared with the existed theorems of LLNs for uncertain random variables, our theorems are the generalised results.
LA - eng
KW - law of large numbers; uncertain random variable; Etemadi type theorem; Marcinkiewicz–Zygmund type theorem
UR - http://eudml.org/doc/299096
ER -

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