Convergence in Distribution for Uncertain Random Variables

A random variable is a measurable function from an uncertainty space to the set of real numbers, which is used to model randomness. An uncertain variable is a measurable function from uncertainty space to the set of real numbers, which is used to describe uncertainty. However, randomness and uncertainty often simultaneously appear in a complex system. Uncertain random variable provides a useful tool to handle such a hybrid case. This concept integrates random variable and uncertain variable into a broader view. For uncertain random variables, a basic and important topic is to discuss the convergence of its sequence. Specifically, this paper focuses on studying the convergence in distribution for a sequence of uncertain random variables without a common chance distribution.