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 ldquokernel type single input rule modules connected fuzzy inference methodrdquo 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.