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

Li Guan, Juan Wei, Hui Min and Junfei Zhang
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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

Mathematics, 2021, vol. 9, issue 11, 1-12

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.

Keywords: set-valued random variables; laws of large numbers; fuzzy metric space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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