International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지

On Generating Fuzzy Systems based on Pareto Multi-objective Cooperative Coevolutionary Algorithm

  • Xing, Zong-Yi (School of Mechanical Engineering/Automation, Nanjing University of Science and Technology) ;
  • Zhang, Yong (School of Mechanical Engineering/Automation, Nanjing University of Science and Technology) ;
  • Hou, Yuan-Long (School of Mechanical Engineering/Automation, Nanjing University of Science and Technology) ;
  • Jia, Li-Min (School of Traffic and Transportation, Beijing Jiaotong University)
  • Published : 2007.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

An approach to construct multiple interpretable and precise fuzzy systems based on the Pareto Multi-objective Cooperative Coevolutionary Algorithm (PMOCCA) is proposed in this paper. First, a modified fuzzy clustering algorithm is used to construct antecedents of fuzzy system, and consequents are identified separately to reduce computational burden. Then, the PMOCCA and the interpretability-driven simplification techniques are executed to optimize the initial fuzzy system with three objectives: the precision performance, the number of fuzzy rules and the number of fuzzy sets; thus both the precision and the interpretability of the fuzzy systems are improved. In order to select the best individuals from each species, we generalize the NSGA-II algorithm from one species to multi-species, and propose a new non-dominated sorting technique and collaboration mechanism for cooperative coevolutionary algorithm. Finally, the proposed approach is applied to two benchmark problems, and the results show its validity.

Keywords

References

  1. J. Casillas, O. Cordon, and F. Herrera, Interpretability Issues in Fuzzy Modeling, Springer, 2003
  2. J. Casillas, O. Cordon, and F. Herrera, Accuracy Improvements in Linguistic Fuzzy Modeling, Springer, 2003
  3. R. Mikut, J. Jakel, and L. Groll, 'Interpretability issues in data-based learning of fuzzy systems,' Fuzzy Sets and Systems, vol. 150, no. 2, pp. 179-197, 2005 https://doi.org/10.1016/j.fss.2004.06.006
  4. H. Wang, S. Kwong, Y. Jin, W. Wei, and K. F. Man, 'Multi-objective hierarchical genetic algorithm for interpretable fuzzy rule-based knowledge extraction,' Fuzzy Sets and System, vol. 149, no. 1, pp. 149-186, 2005 https://doi.org/10.1016/j.fss.2004.07.013
  5. H. Roubos and M. Setnes, 'Compact and transparent fuzzy models and classifiers through iterative complexity reduction,' IEEE Trans. on Fuzzy Systems, vol. 9, no. 4, pp. 516-524, 2001 https://doi.org/10.1109/91.940965
  6. D. D. Nauck, 'Fuzzy data analysis with NEFCLASS,' Approximate Reasoning, vol. 32, no. 2-3, pp.103-130, 2003 https://doi.org/10.1016/S0888-613X(02)00079-8
  7. Y. Jin, 'Fuzzy modeling of high-dimensional systems complexity reduction and interpretability improvement,' Fuzzy Sets and Systems, vol. 8, no. 2, pp. 212-221, 2000 https://doi.org/10.1109/91.842154
  8. Y. Jin, Advanced Fuzzy Systems Design and Applications, Physical-verl, New York, 2003
  9. O. Kaynak, K. Jezernik, and A. Szeghegyi, 'Complexity reduction of rule based models: a survey,' Proc of IEEE Int. Conf. on Fuzzy Systems, pp. 1216-1222, 2002
  10. S. Guillaume, 'Designing fuzzy inference systems from data: An interpretability-oriented review,' IEEE Trans on Fuzzy Systems, vol. 9, no. 3, pp. 426-443, 2001 https://doi.org/10.1109/91.928739
  11. T. Sudkamp, A. Knapp, and J. Knapp, 'Model generation by domain refinement and rule reduction,' IEEE Trans. on Systems, Man, and Cybernetics, vol. 33, no. 1, pp. 45-55, 2003 https://doi.org/10.1109/TSMCB.2003.808186
  12. M. Setnes and H. Hellendoorn, 'Orthogonal transforms for ordering and reduction of fuzzy rules,' Proc of IEEE Int. Conf. on Fuzzy Systems, pp. 700-705, 2000
  13. C. A. Pena and M. Sipper, 'FuzzyCoCo: A cooperative-coevolutionary approach to fuzzy modeling,' IEEE Trans. on Fuzzy Systems, vol. 9, no. 5, pp. 727-737, 2001 https://doi.org/10.1109/91.963759
  14. O. Cordon and F. Herrer, Genetic Fuzzy Systems: Evolutionary Tuning and Learning of Fuzzy Rule Bases, World Scientific, Singapore, 2000
  15. M. R. Delgado and J. Fernando, 'Hierarchical genetic fuzzy systems,' Information Sciences, vol. 136, no. 1-4, pp. 29-52, 2001 https://doi.org/10.1016/S0020-0255(01)00140-2
  16. T. Takagi and M. Sugeno, 'Fuzzy identification of systems and its application to modeling and control,' IEEE Trans. on Systems Man and Cybernetics, vol. 15, no. 1, pp. 116-132, 1985
  17. J. C. Bezdek, Pattern Recognition with Fuzzy Objective Algorithm, Plenum, New York, 1981
  18. D. Gustafson and W. Kessel, 'Fuzzy clustering with a fuzzy covariance matrix,' Proc. of IEEE Conf. on Decision and Control, pp. 761-766, 1979
  19. J. Abonyi, B. Babuska, and F. Szeifert, 'Modified Gath-Geva fuzzy clustering for identification of Takagi-Sugeno fuzzy models,' IEEE Trans. on Systems, Man and Cybernetics, Part B, vol. 32, no. 5, pp. 612-621, 2002 https://doi.org/10.1109/TSMCB.2002.1033180
  20. R. Babuska, Fuzzy Modeling for Control, Kluwer Academic Publishers, Boston, 1998
  21. M. Setnes and R. Babuska, 'Similarity measures in fuzzy rule base simplification,' IEEE Trans. on Systems Man and Cybernetics, vol. 28, no. 3, pp. 376-386, 1998 https://doi.org/10.1109/3477.678632
  22. H. Ishibushi, T. Nakashima, and T. Murata, 'Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems,' IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 29, no. 5, pp. 601-618, 1999 https://doi.org/10.1109/3477.790443
  23. K. Deb, A. Pratap, and S. Agarwal, 'A fast and elitist multiobjective genetic algorithm: NSGA-II,' IEEE Trans. on Evolutionary Computation, vol. 6, no. 2 ,pp. 182-197, 2002 https://doi.org/10.1109/4235.996017
  24. J. D. Knowles and D. Come, 'Approximating the nondominated front using the pareto archived evolution strategy,' Evolutionary Computation, vol. 8, no. 2, pp. 149-172, 2000 https://doi.org/10.1162/106365600568167
  25. E. Zitzler and L. Thiele, 'Multi-objective evolutionary algorithms: A comparative case study and the strength Pareto approach,' IEEE Trans. on Evolutionary Computation, vol. 3, no. 4, pp. 257-271, 1999 https://doi.org/10.1109/4235.797969
  26. M. Potter and A. D. Kenneth, 'Cooperative coevolution: Architecture for evolving coadapted subcomponents,' Evolutionary Computation, vol. 8, no. 1, pp. 1-29, 2000 https://doi.org/10.1162/106365600568086
  27. J. Yen and L. Wang, 'Simplifying fuzzy rule-based models using orthogonal transformation methods,' IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetic, vol. 29, no. 1, pp. 13-24, 1999 https://doi.org/10.1109/3477.740162
  28. H. Roubos and M. Setnes, 'Compact and transparent fuzzy models and classifiers through iterative complexity reduction,' IEEE Trans. on Fuzzy Systems, vol. 9, no. 4, pp. 516-524, 2001 https://doi.org/10.1109/91.940965
  29. M. S. Kim, C. H. Kim, and J. J. Lee, 'Building a fuzzy model with transparent membership functions through constrained evolutionary optimization,' International Journal of Control, Automation, and Systems, vol. 2, no. 3, pp. 298-309, 2004
  30. R. P. Paiva and A. Dourado, 'Interpretability and learning in neuro-fuzzy systems,' Fuzzy Sets and Systems, vol. 147, no. 1, pp. 17-38, 2004 https://doi.org/10.1016/j.fss.2003.11.012