Affiliations: Management Engineering Laboratory, Graduate School of Information, Production and Systems, Waseda University, Kitakyushu, Fukuoka, Japan
Note: [] Corresponding author. Management Engineering Laboratory, Graduate School of Information, Production and Systems, Waseda University, 2-7 Hibikino, Wakamatsu, Kitakyushu 808-0135, Fukuoka, Japan. Tel.: +81 80 3228 1030; Fax: +81 93 692 5179. E-mails: smwangips@gmail.com (S. Wang); junzow@osb.att.ne.jp (J. Watada).
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.
Keywords: Limit theorem, Law of large numbers, Fuzzy random variable, Archimedean t-norm
