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

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

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 Hau...

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Main Authors: Li Guan, Juan Wei, Hui Min, Junfei Zhang
Format: Article
Language:English
Published: MDPI AG 2021-05-01
Series:Mathematics
Subjects:
set-valued random variables
laws of large numbers
fuzzy metric space
Online Access:https://www.mdpi.com/2227-7390/9/11/1192
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spelling doaj-9053391b32464385bd5fc51f4c8608662021-06-01T01:01:41ZengMDPI AGMathematics2227-73902021-05-0191192119210.3390/math9111192The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric SpaceLi Guan0Juan Wei1Hui Min2Junfei Zhang3Faculty of Science, College of Statistics and Data Science, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, ChinaFaculty of Science, College of Statistics and Data Science, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, ChinaFaculty of Science, College of Statistics and Data Science, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, ChinaSchool of Statistics and Mathematics, Central University of Finance and Economics, 39 South College Road, Haidian District, Beijing 100081, ChinaIn 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.https://www.mdpi.com/2227-7390/9/11/1192set-valued random variableslaws of large numbersfuzzy metric space
collection DOAJ
language English
format Article
sources DOAJ
author Li Guan
Juan Wei
Hui Min
Junfei Zhang
spellingShingle Li Guan
Juan Wei
Hui Min
Junfei Zhang
The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space
Mathematics
set-valued random variables
laws of large numbers
fuzzy metric space
author_facet Li Guan
Juan Wei
Hui Min
Junfei Zhang
author_sort Li Guan
title The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space
title_short The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space
title_full The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space
title_fullStr The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space
title_full_unstemmed The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space
title_sort strong laws of large numbers for set-valued random variables in fuzzy metric space
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-05-01
description 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.
topic set-valued random variables
laws of large numbers
fuzzy metric space
url https://www.mdpi.com/2227-7390/9/11/1192
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