The modes of convergence in the approximation of fuzzy random optimization problems

Authors:
Yan-Kui Liu;Zhi-Qiang Liu;Jinwu Gao
Affiliations:
Hebei University, College of Mathematics & Computer Science, 071002, Baoding, Hebei, China;City University of Hong Kong, School of Creative Media, 071002, Hong Kong, Hebei, China;Renmin University of China, School of Information, 100872, Beijing, Hebei, China
Venue:
Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special issue on Uncertainty Analysis and Decision Making; Guest Editors: Yan-Kui Liu, Baoding Liu, Jinwu Gao
Year:
2008

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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.