Abstract: In order to solve the problem that the number of rules in intelligent control and prediction based on cloud model increases exponentially with the number of variables involved，a hierarchical cloud inference system with uncertainty is proposed and its approximation performance is testified.The hierarchical cloud inference system with uncertainty is constructed using the new reasoning model about uncertainty based on cloud theory and analytical expression is given，then the capability of the hierarchical cloud inference system with uncertainty approximating any continuous function on a compact set is testified.The result shows the computational expression of output results of the hierarchical cloud inference system with uncertainty satisfies the three hypothetic conditions of Stone-Weirstrass theorem and the system has global approximation property.

Key words: cloud model, hierarchical cloud inference system, approximation performance, uncertainty reasoning

摘要： 为了解决目前基于云模型的智能控制和预测中规则数目随系统变量的个数呈指数增长的问题，设计分层云不确定性推理系统，并证明该系统的逼近性能。采用基于云理论的新的不确定性推理模型来设计分层云不确定性推理系统并给出解析表达式。证明分层云不确定性推理系统对致密集上函数的逼近能力。结果表明：分层云不确定性推理系统的输出结果计算式满足Stone-Weirstrass定理的3个假设条件，具有万能逼近性质。

关键词: 云模型, 分层云推理系统, 逼近性能, 不确定性推理