Abstract
The objective of this paper is to derive some limit theorems of fuzzy random variables under the extension principle associated with continuous Archimedean triangular norms (t-norms). First of all, some convergence theorems for the sum of fuzzy random variables in chance measure and expected value are proved respectively based on the arithmetics of continuous Archimedean triangular norms. Then, a law of large numbers for fuzzy random variables is established by using the obtained convergence theorems. The results of the derived law of large numbers can degenerate to the strong laws of large numbers for random variables and fuzzy variables, respectively.
| Original language | English |
|---|---|
| Pages (from-to) | 233-242 |
| Number of pages | 10 |
| Journal | Journal of Intelligent and Fuzzy Systems |
| Volume | 21 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2010 |
Keywords
- Archimedean t-norm
- Fuzzy random variable
- Law of large numbers
- Limit theorem
ASJC Scopus subject areas
- Artificial Intelligence
- Engineering(all)
- Statistics and Probability