SIRMs connected fuzzy inference method using kernel method

Single Input Rule Modules connected fuzzy inference method (SIRMs method, for short) by Yubazaki can decrease the number of fuzzy rules drastically in comparison with the conventional fuzzy inference methods. Seki et al. have proposed functional type single input rule modules connected fuzzy inference method (functional type SIRMs method, for short) which generalizes the consequent part of SIRMs method to function. However, these SIRMs methods can not be applied to XOR (Exclusive OR). In this paper, we propose “kernel type single input rule modules connected fuzzy inference method” which uses kernel trick to SIRMs method, and show that this method can treat XOR. Further, learning algorithm of the proposed SIRMs method is derived by using the steepest descent method, and is shown to be superior to the one of conventional SIRMs method and kernel perceptron by applying to identification of nonlinear functions.

I. Introduction

As for “if-then” rules in traditional fuzzy inference methods [1], all the input items of the system are set to antecedent part, and all output items are set to consequent part. Therefore, the problem is that the number of fuzzy rules becomes very huge and so the setup and adjustment of fuzzy rules become difficult. On the other hand, “Single Input Rule Modules connected type fuzzy inference method” (SIRMs method) by Yubazaki et al. [2]–[5] which unifies the inference output from fuzzy rule modules of one input type “if-then” form can reduce the number of fuzzy rules drastically. The method has been applied to nonlinear function identification, control of a first order lag system with dead time, orbital pursuit control of a non-restrained object, and stabilization control of a handstand system etc., and good results are obtained. However, since the number of rules of SIRMs method were limited compared to traditional inference method, inference results gained by SIRMs method were simple in general.