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.

随机变量和不确定变量分别用于建模随机性和不确定性。虽然随机性和不确定性总是在同一复杂系统中共存。随着随机变量和不确定变量的发展，引入不确定随机变量作为同时处理随机性和不确定性的复杂现象的工具。对于不确定的随机变量，一个基本且重要的主题是讨论其序列的收敛性。具体来说，本文重点研究具有随机机会不独立的具有不同机会分布的不确定随机序列序列的分布收敛性。并且本文的结果是对现有文献的概括。研究了收敛定理之间的关系。此外，