Uniform integrability of fuzzy variable sequences

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.