An Extended Method of SIRMs Connected Fuzzy Inference Method Using Kernel Method

Hirosato SEKI  Fuhito MIZUGUCHI  Satoshi WATANABE  Hiroaki ISHII  Masaharu MIZUMOTO  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A    No.10    pp.2514-2521
Publication Date: 2009/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.2514
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: Nonlinear Problems
Keyword: 
fuzzy inference systems,  SIRMs connected fuzzy inference method,  kernel trick,  

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Summary: 
The single input rule modules connected fuzzy inference method (SIRMs method) by Yubazaki et al. can decrease the number of fuzzy rules drastically in comparison with the conventional fuzzy inference methods. Moreover, Seki et al. have proposed a functional-type SIRMs method which generalizes the consequent part of the SIRMs method to function. However, these SIRMs methods can not be applied to XOR (Exclusive OR). In this paper, we propose a "kernel-type SIRMs method" which uses the kernel trick to the SIRMs method, and show that this method can treat XOR. Further, a learning algorithm of the proposed SIRMs method is derived by using the steepest descent method, and compared with the one of conventional SIRMs method and kernel perceptron by applying to identification of nonlinear functions, medical diagnostic system and discriminant analysis of Iris data.