Convergence criteria and convergence relations for sequences of fuzzy random variables

Authors:
Yan-Kui Liu;Jinwu Gao
Affiliations:
College of Mathematics and Computer Science, Hebei University, Baoding, Hebei, China;School of Information, Renmin University of China, Beijing, China
Venue:
FSKD'05 Proceedings of the Second international conference on Fuzzy Systems and Knowledge Discovery - Volume Part I
Year:
2005

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Abstract

Fuzzy random variable is a measurable map from a probability space to a collection of fuzzy variables. In this paper, we first present several new convergence concepts for sequences of fuzzy random variables, including convergence almost sure, uniform convergence, almost uniform convergence, convergence in mean chance, and convergence in mean chance distribution. Then, we discuss the criteria for convergence almost sure, almost uniform convergence, and convergence in mean chance. Finally, we deal with the relationship among various types of convergence.