Abstract
This paper proposes a method to organize a hierarchical structure of fuzzy model with the genetic algorithm and back-propagation method. The number of fuzzy rules increases exponentially as the number of input variables increases. Hance the fuzzy system with many input variables has extremely large number of fuzzy rules.Hierarchical structure of fuzzy reasoning is one of the methods to reduce the number of fuzzy rules and membership functions. However the hierarchical structure cannot be made without considering the relation among input and output variables. The proposed method can organize the suitale hierarchical structure for the relation among input and output variables. It is based on the genetic algorithm with an evaluation function as a strategy that adopts a system with fewer fuzzy rules and membership functions and more accurate outputs. The proposed method is applied to the approximation problems of multi-dimensional nonlinear functions in order to show the effectiveness.
