On the Learning Method, Properties of the Extended Functional-Type SIRMs Connected Fuzzy Inference Model and Their Application to a Medical Diagnosis System
Diederik van Krieken*, Hirosato Seki**, and Masahiro Inuiguchi**
*University of Groningen
43-2 John Franklinstraat, Amsterdam 1056 SX, the Netherlands
**Graduate School of Engineering Science, Osaka University
1-3 Machikaneyama-cho, Toyonaka, Osaka 560-8531, Japan
Seki et al. have proposed the functional type single input rule modules fuzzy inference model (functional-type SIRMs model, for short) which generalized consequent part of SIRMs model to function. However, it is too strict to satisfy the equivaence conditions of T–S inference model. Therefore, this paper proposes an extended functional-type SIRMs model (EF-SIRMs, for short) in which the consequent part of the functional-type SIRMs model is extended to a function with 1 dimensional polynomial from a function with n dimensional polynomial, and its properties are clarified. Further, it shows the ability of this model becomes greatly larger than that of ordinary functional-type SIRMs model. Moreover, it proposes a learning method of the EF-SIRMs model, and it is applied to a medical diagnosis, and compared with the conventional SIRMs models.
-  N. Yubazaki, J. Yi, M. Otani, and K. Hirota, “SIRMs dynamically connected fuzzy inference model and its applications,” Proc. IFSA’97, Vol.3, pp. 410-415, Prague, Czech, 1997.
-  J. Yi, N. Yubazaki, and K. Hirota, “Upswing and stabilization control of inverted pendulum and cart system by the SIRMs dynamically connected fuzzy inference model,” Proc. 1999 IEEE Int. Conf. on Fuzzy Syst., Vol.1, pp. 400-405, 1999.
-  J. Yi, N. Yubazaki, and K. Hirota, “A proposal of SIRMs dynamically connected fuzzy inference model for plural input fuzzy control,” Fuzzy Sets Syst., Vol.125, No.1, pp. 79-92, 2002.
-  J. Yi, N. Yubazaki, and K. Hirota, “A new fuzzy controller for stabilization of parallel-type double inverted pendulum system,” Fuzzy Sets Syst., Vol.126, No.1, pp. 105-119, 2002.
-  H. Seki and M. Mizumoto, “On the equivalence conditions of fuzzy inference methods – part 1: basic concept and definition” IEEE Trans. on Fuzzy Sust., Vol.19, No.6, pp. 1097-1106, 2011.
-  H. Seki, H. Ishii, and M. Mizumoto, “On the generalization of single input rule modules connected type fuzzy reasoning method,” IEEE Trans. Fuzzy Syst., Vol.16, No.5, pp. 1180-1187, 2008.
-  H. Seki, H. Ishii, and M. Mizumoto, “On the monotonicity of fuzzy-inference methods related to T–S inference method,” IEEE Trans. Fuzzy Syst., Vol.18, No.3, pp. 629-634, 2010.
-  H. Seki, H. Ishii, and M. Mizumoto, “Nonlinear identification and medical diagnosis system using functional-type SIRMs connected fuzzy inference method,” International Journal of Innovative Computing, Information and Control, Vol.6, No.10, pp. 5275-5286, 2010.
-  T. Takagi and M. Sugeno, “Fuzzy identification of systems and its Applications to modeling and control,” IEEE Trans. Syst., Man, Cybern., Vol.SMC-15, No.1, pp. 116-132, 1985.
-  H. Ichihashi, “Iterative fuzzy modeling and a hierarchical network,” Proc. 4th IFSA Congress of Engineering, pp. 49-52, 1991.
-  L. X. Wang and J. M. Mendel, “Back-Propagation fuzzy system as nonlinear dynamic system identifiers,” in Proc. 1992 IEEE Int. Conf. Fuzzy Syst., pp. 1409-1416, 1992.
-  X. Cui and K. G. Shin, “Direct control and coordination using neural networks,” IEEE Trans. Syst., Man, Cybern., Vol.23, No.3, pp. 686-697, 1993.
-  C. F. Juang, “A TSK type recurrent fuzzy network for dynamic systems processing by neural network and genetic algorithms,” IEEE Trans. Fuzzy Syst., Vol.10, No.2, pp. 155-170, 2002.
-  W. Yu and X. Li, “Fuzzy identification using fuzzy neural networks with stable learning algorithms,” IEEE Trans. Fuzzy Syst., Vol.12, No.3, pp. 411-420, 2004.
-  D. F. Andrews and A. M. Herzberg, “Data: A collection of problems from many fields for the students and research worker,” Springer, 1985.