Modeling Approach Based on Modular Fuzzy Model
Toshihiko Watanabe* and Hirosato Seki**
*Department of Electrical and Electronic Engineering, Faculty of Engineering, Osaka Electro-Communication University, 18-8 Hatsu-cho, Neyagawa, Osaka 572-8530, Japan
**Department of Mathematical Sciences, Kwansei Gakuin University, 2-1 Gakuen, Sanda, Hyogo 669-1337, Japan
Fuzzy modeling is one of the most important techniques for nonlinear modeling. SIRMs (Single Input Rule Modules) has been studied as a useful modeling method for real-life applications such as control and pattern recognition. Although the SIRMs is a practical modeling approach based on fuzzy reasoning, its performance is adversely affected by high-dimensional or complicated characteristics of the problems. The modular fuzzy model is an extension of the SIRMs for overcoming such a performance problem. In this paper, we study a modeling approach based on the modular fuzzy model by extending the SIRMs architecture. We show that the construction of error objective functions for modeling the modular fuzzy model and the SIRMs affects the prediction performance of the model. Through numerical experiments on modeling problems and reinforcement learning problems, we study the model construction based on the error objective functions. We find that the error objective function should be selected according to the number of dimensions of projection in the modular fuzzy model.
-  E. H. Mamdani, “Application of Fuzzy Algorithms for Control of Simple Dynamic Plant,” Proc. IEEE, Vol.121, No.12, pp. 1585-1588, 1974.
-  T. Takagi and M. Sugeno, “Fuzzy Identification of Systems and Its Applications to Modeling and Control,” IEEE Trans. on Syst., Man, and Cybern., Vol.15, pp. 116-132, 1985.
-  A. N. Jha, A. S. Saxena, and V. S. Rajamani, “Parameter Estimation Algorithms for Bilinear and Non-linear Systems UsingWalsh Functions – Recursive Approach,” Int. J. Systems Sci., Vol.23, No.2, pp. 283-290, 1992.
-  W. T.Miller, F. G. Glanz, and L. G. Kraft, “Application of a General Learning Algorithm to the Control of Robotic Manipulators,” Int. J. of Robotic Research, Vol.6, No.2, pp. 84-98, 1987.
-  N. Yubazaki, J. Yi, M. Otani, and K. Hirota, “SIRMs Dynamically Connected Fuzzy Inference Model and Its Applications,” Proc. IFSA’97, No.3, pp. 410-415, 1997.
-  H. Seki, H. Ishii, and M. Mizumoto, “On the Generalization of Single Input Rule Modules Connected Type Fuzzy Reasoning Method,” IEEE Trans. on Fuzzy Systems, Vol.16, No.5, pp. 1180-1187, 2008.
-  T.Watanabe and Y. Takahashi, “Hierarchical Reinforcement Learning Using aModular Fuzzy Model for Multi-Agent Problem,” Proc. of the 2007 IEEE Int, Conf. on Syst., Man, and Cybern., pp. 1681- 1686, 2007.
-  T. Watanabe and R. Fujioka, “Collaborative Filtering Based on Modular Fuzzy Model Concept,” Proc. Joint 4th Int. Conf. on Soft Computing and Intelligent Systems and 9th Int. Symp. on Advanced Intelligent Systems (SCIS&ISIS 2008), pp. 1350-1354, 2008.
-  T.Watanabe and T.Wada, “Reinforcement Learning Based onModular Fuzzy Model with Gating Unit,” Proc. 2008 IEEE Int. Conf. Syst., Man, Cybern., pp. 1806-1811, 2008.
-  R. A. Jacobs, M. I. Jordan, and A. G. Barto, “Task Decomposition through Competition in a Modular Connectionist Architecture: The What andWhere Vision Tasks,” Neural Computation, Vol.3, pp. 79-87, 1991.
-  G. Auda and M. Kamel, “Modular Neural Networks: A Survey,” Int. J. of Neural Systems, Vol.9, No.2, pp. 129-151, 1999.
-  Y. Freund and R. E. Schapire, “A Decision-Theoretic Generalization of On-line Learning and an Application to Boosting,” J. of Computer and System Sciences, Vol.55, No.1, pp. 119-139, 1997.
-  L. Breiman, “Bagging Predictors,” Machine Learning, Vol.24, No.2, pp. 123-140, 1996.
-  S. Wu, M. J. Er, and Y. Gao, “A Fast Approach for Automatic Generation of Fuzzy Rules by Generalized Dynamic Fuzzy Neural Networks,” IEEE Trans. Fuzzy Systems, Vol.9, pp. 578-594, 2001.
-  H. Seki, F. Mizuguchi, S. Watanabe, H. Ishii, and M. Mizumoto, “SIRMs Connected Fuzzy Inference Method Using Kernel Method,” Proc. 2008 IEEE Int. Conf. Syst., Man, Cybern., pp. 1776-1781, 2008.
-  H. Ichihashi and T. Watanabe, “Learning Control System by a Simplified Fuzzy Reasoning Model,” Proc. of the 3rd Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp. 417-419, 1990.
-  P. Y. Glorennec, “Reinforcement Learning: Overview,” Proc. of ESIT, pp. 17-35, 2000.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.