scholarly journals Strong Law of Large Numbers for Fuzzy Random Variables in Fuzzy Metric Space

2020 ◽  
Vol 20 (4) ◽  
pp. 278-289
Author(s):  
Reza Ghasemi ◽  
Mohammad Reza Rabiei ◽  
Ahmad Nezakati
Keyword(s):  
Metric Space ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Fuzzy Metric Space ◽  
Fuzzy Random Variables ◽  
Strong Law ◽  
Fuzzy Metric ◽  
Large Numbers ◽  
Fuzzy Random

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
Keyword(s):  
Metric Space ◽  
Convex Sets ◽  
Law Of Large Numbers ◽  
Compact Convex ◽  
Random Sets ◽  
Fuzzy Metric Space ◽  
Strong Law ◽  
Fuzzy Metric ◽  
Large Numbers ◽  
Fuzzy Random

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.

scholarly journals Law of large numbers for the sequence of uncorrelated fuzzy random variables

2021 ◽  
pp. 1-8
Author(s):  
Li Guan ◽  
Jinping Zhang ◽  
Jieming Zhou
Keyword(s):  
Law Of Large Numbers ◽  
Hausdorff Metric ◽  
Random Variables ◽  
Fuzzy Random Variables ◽  
Strong Law ◽  
Fuzzy Variables ◽  
Large Numbers ◽  
The Law ◽  
Fuzzy Random

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.

scholarly journals Limit theorems for fuzzy random variables

1986 ◽  
Vol 407 (1832) ◽  
pp. 171-182 ◽  
Keyword(s):  
Banach Space ◽  
Limit Theorem ◽  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Embedding Theorems ◽  
Fuzzy Random Variables ◽  
Strong Law ◽  
Large Numbers ◽  
Fuzzy Random

A strong law of large numbers and a central limit theorem are proved for independent and identically distributed fuzzy random variables, whose values are fuzzy sets with compact levels. The proofs are based on embedding theorems as well as on probability techniques in Banach space.

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