Affiliations: [a]
College of People’s Armed Force, Hebei University, Shijiazhuang, China
| [b]
College of Mathematics and Information Science, Hebei University, Baoding, China
| [c]
School of Information, Renmin University of China, Beijing, China
Correspondence:
[*]
Corresponding author. Rui-Sheng Wang, School of Information, Renmin University of China, Beijing 100872, China. E-mail: wangrsh@amss.ac.cn.
Abstract: A fuzzy variable is a measurable function from a possibility measure space to a set of real numbers. It is a useful tool to describe the fuzziness of phenomena in a decision making process. In this paper, we focus on investigating the properties of sequences of fuzzy variables. The concepts of uniform integrability, uniform absolute continuity and uniform boundedness are introduced for fuzzy variable sequences, and then the relations among them are discussed. As the applications of these concepts, we also present several convergence theorems for sequences of fuzzy variables by using uniform integrability. Specifically, the relations between uniform integrability and convergence properties, such as convergence in measure, convergence in mean, and convergence almost surely, are discussed.
