Separable Approximation Property of Hierarchical Fuzzy Systems

摘要

This paper discusses the capabilities of standard hierarchical fuzzy systems to approximate continuous functions with natural hierarchical structure. The separable approximation property of hierarchical fuzzy systems is proved, that is, the construction of a hierarchical fuzzy system with required approximation accuracy can be achieved by the separate construction of each sub-system with required approximation accuracy. This property provides a simple method to construct hierarchical fuzzy systems for function approximation. Based on the separable approximation property, it is further proved the structure approximation property of hierarchical fuzzy systems.