A Strong Law of Large Numbers for Random Sets in Fuzzy Banach Space
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...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2020/8185061 |
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| author | R. Ghasemi A. Nezakati M. R. Rabiei |
| author_facet | R. Ghasemi A. Nezakati M. R. Rabiei |
| author_sort | R. Ghasemi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a5f2d26ce88d4ca1a7e2ff57acf38041 |
| institution | Kabale University |
| issn | 1687-7101 1687-711X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-a5f2d26ce88d4ca1a7e2ff57acf380412025-02-03T01:28:22ZengWileyAdvances in Fuzzy Systems1687-71011687-711X2020-01-01202010.1155/2020/81850618185061A Strong Law of Large Numbers for Random Sets in Fuzzy Banach SpaceR. Ghasemi0A. Nezakati1M. R. Rabiei2Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, IranFaculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, IranFaculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, IranThe 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.http://dx.doi.org/10.1155/2020/8185061 |
| spellingShingle | R. Ghasemi A. Nezakati M. R. Rabiei A Strong Law of Large Numbers for Random Sets in Fuzzy Banach Space Advances in Fuzzy Systems |
| title | A Strong Law of Large Numbers for Random Sets in Fuzzy Banach Space |
| title_full | A Strong Law of Large Numbers for Random Sets in Fuzzy Banach Space |
| title_fullStr | A Strong Law of Large Numbers for Random Sets in Fuzzy Banach Space |
| title_full_unstemmed | A Strong Law of Large Numbers for Random Sets in Fuzzy Banach Space |
| title_short | A Strong Law of Large Numbers for Random Sets in Fuzzy Banach Space |
| title_sort | strong law of large numbers for random sets in fuzzy banach space |
| url | http://dx.doi.org/10.1155/2020/8185061 |
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