Efficient Parametric Adjustment of Fuzzy Inference System Using Error Backpropagation Method

This paper presents a new methodology for the adjustment of fuzzy inference systems, which uses technique based on error back-propagation method. The free parameters of the fuzzy inference system, such as its intrinsic parameters of the membership function and the weights of the inference rules, are automatically adjusted. This methodology is interesting, not only for the results presented and obtained through computer simulations, but also for its generality concerning to the kind of fuzzy inference system used. Therefore, this methodology is expandable either to the Mandani architecture or also to that suggested by Takagi-Sugeno. The validation of the presented methodology is accomplished through estimation of time series and by a mathematical modeling problem. More specifically, the Mackey-Glass chaotic time series is used for the validation of the proposed methodology.

[1]  Hiok Chai Quek,et al.  Falcon: neural fuzzy control and decision systems using FKP and PFKP clustering algorithms , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[2]  Chee Kheong Siew,et al.  Universal Approximation using Incremental Constructive Feedforward Networks with Random Hidden Nodes , 2006, IEEE Transactions on Neural Networks.

[3]  D. Marquardt An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[4]  M. Sugeno,et al.  Structure identification of fuzzy model , 1988 .

[5]  Abraham Kandel,et al.  Complex fuzzy logic , 2003, IEEE Trans. Fuzzy Syst..

[6]  Rajani K. Mudi,et al.  A new scheme for fuzzy rule-based system identification and its application to self-tuning fuzzy controllers , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[7]  Suzanna Becker,et al.  Unsupervised Learning Procedures for Neural Networks , 1991, Int. J. Neural Syst..

[8]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[9]  Kotaro Hirasawa,et al.  Relation between weight initialization of neural networks and pruning algorithms: case study on Mackey-Glass time series , 2001, IJCNN'01. International Joint Conference on Neural Networks. Proceedings (Cat. No.01CH37222).

[10]  Serge Guillaume,et al.  Designing fuzzy inference systems from data: An interpretability-oriented review , 2001, IEEE Trans. Fuzzy Syst..

[11]  Massimo Panella,et al.  An input-output clustering approach to the synthesis of ANFIS networks , 2005, IEEE Transactions on Fuzzy Systems.

[12]  Jyh-Shing Roger Jang,et al.  ANFIS: adaptive-network-based fuzzy inference system , 1993, IEEE Trans. Syst. Man Cybern..

[13]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[14]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[15]  Chi-Kwong Li,et al.  An approach to tune fuzzy controllers based on reinforcement learning for autonomous vehicle control , 2005, IEEE Transactions on Intelligent Transportation Systems.

[16]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[17]  Yoichi Hori,et al.  An Algorithm for Extracting Fuzzy Rules Based on RBF Neural Network , 2006, IEEE Transactions on Industrial Electronics.

[18]  Constantin V. Negoita,et al.  On Fuzzy Systems , 1978 .

[19]  Michio Sugeno,et al.  A fuzzy-logic-based approach to qualitative modeling , 1993, IEEE Trans. Fuzzy Syst..

[20]  Walenty Ostasiewicz On fuzzy sets , 1981 .

[21]  Ryotaro Kamimura,et al.  Improving generalization performance by information minimization , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

[22]  María José del Jesús,et al.  Genetic tuning of fuzzy rule deep structures preserving interpretability and its interaction with fuzzy rule set reduction , 2005, IEEE Transactions on Fuzzy Systems.