scholarly journals A Strong Law of Large Numbers for Random Sets in Fuzzy Banach Space

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
R. Ghasemi ◽  
A. Nezakati ◽  
M. R. Rabiei

The main purpose of this paper is to consider the strong law of large numbers for random sets in fuzzy metric space. Since many years ago, limited theorems have been expressed and proved for fuzzy random variables, but despite the uncertainty in fuzzy discussions, the nonfuzzy metric space has been used. Given that the fuzzy random variable is defined on the basis of random sets, in this paper, we generalize the strong law of large numbers for random sets in the fuzzy metric space. The embedded theorem for compact convex sets in the fuzzy normed space is the most important tool to prove this generalization. Also, as a result and by application, we use the strong law of large numbers for random sets in the fuzzy metric space for the bootstrap mean.

Author(s):  
Li Guan ◽  
Jinping Zhang ◽  
Jieming Zhou

This work proposes the concept of uncorrelation for fuzzy random variables, which is weaker than independence. For the sequence of uncorrelated fuzzy variables, weak and strong law of large numbers are studied under the uniform Hausdorff metric d H ∞ . The results generalize the law of large numbers for independent fuzzy random variables.


Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1192
Author(s):  
Li Guan ◽  
Juan Wei ◽  
Hui Min ◽  
Junfei Zhang

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.


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