Convergence in Distribution for Uncertain Random Sequences with Dependent Random Variables

Random variables and uncertain variables are respectively used to model randomness and uncertainty. While randomness and uncertainty always coexist in a same complex system. As an evolution of random variables and uncertain variables, uncertain random variable is introduced as a tool to deal with complex phenomena including randomness and uncertainty simultaneously. 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 sequences with different chance distributions where random variables are not independent. And the result of this paper is a generalization of the existing literature. Relations among convergence theorems are studied. Furthermore, the theorems are explained by several examples.