Hierarchical fuzzy systems as universal approximators

A way to deal with the rule-explosion problem is to use the hierarchical fuzzy systems. In this paper, the hierarchical fuzzy system is constructed first and the property of the hierarchical system is discussed. Then the error properties of the polynomial and hierarchical polynomial are given. Based on these properties, the universal approximation property of the hierarchical fuzzy systems is proved from the mapping point of view. It is concluded that we can get more general sufficient approximation theorem, based on the Stone-Weierstrass Theorem.