Fuzzy Regression Analysis Using Neural Networks and Its Application

Abstract

When we attempt to model a complex system including human as an important component, it may be difficult to represent the system by a deterministic mathematical model. The main reason of this difficulty is that the system itself inherently has some fuzziness concerning subjective judgement of human. As a promising modelling method to cope with this difficulty, the concept of fuzzy regression was proposed and various methods were developed. In this paper, we propose a fuzzy regression method using multilayer neural networks. Since multilayer neural networks have high capability as an approximate realization tool of nonlinear mappings, the proposed method has higher flexibility than fuzzy linear regression models. First we propose learning algorithms to identify a nonlinear interval model which approximately includes all the given input-output data. Next we propose methods to derive a fuzzy model from the identified interval model. Last the proposed method is applied to a quality evaluation problem of injection moldings. The fuzzy relation between subjective ratings of the quality given by experts and gap depths of weld-lines is analyzed using the proposed method and its modelling ability is demonstrated.