模糊系统逼近理论的发展现状

Development of Approximation Theory of Fuzzy Systems

综述了近年来模糊系统逼近理论的主要研究成果,包括Madani型和T-S型模糊系统具有通用逼近性的存在性定理、充分条件和必要条件,以及模糊系统具有通用逼近性的本质。在此基础上,进一步介绍了目前有效的几种模糊系统构造方法:自适应模糊逻辑系统方法、自适应神经模糊推理系统(ANFIS)方法、模糊聚类法、模糊树方法。最后对该理论的未来发展方向给出了分析和展望。

The main results on the approximation theory of fuzzy systems up to date were reviewed and analyzed. These results include existence theorems, sufficient conditions, necessary conditions and the nature on both Madanifuzzy systems and T-S fuzzy systems as function approximators. Moreover several effective approaches of fuzzy systems construction were introduced, including the adaptive-fuzzy-logic-system approach, adaptive-network-based fuzzy system （ANFIS）.approach, fuzzy clustering approach and binary linear fuzzy tree structure approach. In the end, some directs of its development were proposed.