The modes of convergence in the approximation of fuzzy random optimization problems |
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| Authors: | Yan-Kui Liu Zhi-Qiang Liu Jinwu Gao |
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| Affiliation: | (1) College of Mathematics & Computer Science, Hebei University, 071002 Baoding, Hebei, China;(2) School of Creative Media, City University of Hong Kong, Hong Kong, China;(3) School of Information, Renmin University of China, 100872 Beijing, China |
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| Abstract: | To develop the approximation approach to fuzzy random optimization problems, it is required to introduce the modes of convergence in fuzzy random theory. For this purpose, this paper first presents several novel convergence concepts for sequences of fuzzy random variables, such as convergence in chance, convergence in distribution and convergence in optimistic value; then deals with the convergence criteria and convergence relations among various types of convergence. Finally, we deal with the convergence theorems for sequences of integrable fuzzy random variables, including dominated convergence theorem and bounded convergence theorem. |
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| Keywords: | Fuzzy random variable Convergence criteria Convergence relationship Dominated convergence theorem |
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