A Strong Law of Large Numbers for Random Sets in Fuzzy Banach Space. (10th August 2020)

• Record Type: Journal Article
• Authors: Ghasemi, R.; Nezakati, A.; Rabiei, M. R.
• Other Names: Honda Katsuhiro Academic Editor.
• Is Part Of: Advances in fuzzy systems. Volume 2020(2020)
• Publication Date: 2020-08-10
• Subjects: Fuzzy systems -- Periodicals; Systèmes flous; Fuzzy systems; Periodicals; 511.313
• DOI: 10.1155/2020/8185061
• Languages: English
• ISSNs: 1687-7101

Abstract

Abstract : 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.