Efficient Parametric Adjustment of Fuzzy Inference System Using Unconstrained Optimization

  • Ivan Nunes da Silva
  • Rogerio Andrade Flauzino
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4507)


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.


Fuzzy systems tuning algorithm system optimization 


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  1. 1.
    Guillaume, S.: Designing Fuzzy Inference Systems from Data: An Interpretability-Oriented Review. IEEE Trans. Fuzzy Systems 9, 426–443 (2001)CrossRefGoogle Scholar
  2. 2.
    Er, M.J., Deng, C.: Online Tuning of Fuzzy Inference Systems Using Dynamic Fuzzy Q-learning. IEEE Trans. on Systems, Man and Cybernetics (Part B) 34, 1478–1489 (2004)CrossRefGoogle Scholar
  3. 3.
    Casillas, J., Cordon, O., del Jesus, M.J., Herrera, F.: Genetic Tuning of Fuzzy Rule Deep Structures Preserving Interpretability and Its Interaction with Fuzzy Rule Set Reduction. IEEE Trans. on Fuzzy Systems 13, 13–29 (2005)CrossRefGoogle Scholar
  4. 4.
    Pal, K., Mudi, R.K., Pal, N.R.: A New Scheme for Fuzzy Rule-Based System Identification and Its Application to Self-Tuning Fuzzy Controllers. IEEE Trans. on Systems, Man and Cybernetics (Part B) 32, 470–482 (2004)CrossRefGoogle Scholar
  5. 5.
    Dai, X., Li, C.K., Rad, A.B.: An Approach to Tune Fuzzy Controllers Based on Reinforcement Learning for Autonomous Vehicle Control. IEEE Trans. on Intelligent Transportation Systems 6, 285–293 (2005)CrossRefGoogle Scholar
  6. 6.
    Tung, W.L., Quek, C.: Falcon: Neural Fuzzy Control and Decision Systems Using FKP and PFKP Clustering Algorithms. IEEE Trans. on Systems, Man and Cybernetics, Part B 34, 686–695 (2004)CrossRefGoogle Scholar
  7. 7.
    Wan, W., Hirasawa, K., Hu, J., Murata, J.: Relation Between Weight Initialization of Neural Networks and Pruning Algorithms: Case Study on Mackey-Glass Time Series. In: International Joint Conference on Neural Networks, vol. 3, pp. 1750–1755 (2001)Google Scholar
  8. 8.
    Bertsekas, D.P.: Nonlinear Programming, 2nd edn. Athena Scientific, Belmont (1999)zbMATHGoogle Scholar
  9. 9.
    Marquardt, D.: An Algorithm for Least Squares Estimation of Nonlinear Parameters. J. Soc. Ind. Appl. Math. 11, 431–441 (1963)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Mackey, M.C., Glass, L.: Oscillation and Chaos in Physiological Control Sciences. Science 197, 287–289 (1977)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ivan Nunes da Silva
    • 1
  • Rogerio Andrade Flauzino
    • 2
  1. 1.University of São Paulo, Department of Electrical Engineering, CP 359, CEP 13566.590, São Carlos, SPBrazil
  2. 2.São Paulo State University, Department of Production Engineering, CP 473, CEP 17033.360, Bauru, SPBrazil

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