TY - JOUR
T1 - T-norm-based limit theorems for fuzzy random variables
AU - Wang, S.
AU - Watada, J.
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
KW - Archimedean t-norm
KW - Fuzzy random variable
KW - Law of large numbers
KW - Limit theorem
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U2 - 10.3233/IFS-2010-0446
DO - 10.3233/IFS-2010-0446
M3 - Article
AN - SCOPUS:77954476069
SN - 1064-1246
VL - 21
SP - 233
EP - 242
JO - Journal of Intelligent and Fuzzy Systems
JF - Journal of Intelligent and Fuzzy Systems
IS - 4
ER -