Genetically Opimized Self-Organizing Fuzzy Polynomial Neural Networks Based on Fuzzy Polynomial Neurons

퍼지다항식 뉴론 기반의 유전론적 최적 자기구성 퍼지 다항식 뉴럴네트워크

  • 박호성 (원광대학 제어계측공학과) ;
  • 이동윤 (중부대학 정보통신공학) ;
  • 오성권 (원광대학 전기전자ㆍ정보공학부)
  • Published : 2004.08.01

Abstract

In this paper, we propose a new architecture of Self-Organizing Fuzzy Polynomial Neural Networks (SOFPNN) that is based on a genetically optimized multilayer perceptron with fuzzy polynomial neurons (FPNs) and discuss its comprehensive design methodology involving mechanisms of genetic optimization, especially genetic algorithms (GAs). The proposed SOFPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional SOFPNNs. The design procedure applied in the construction of each layer of a SOFPNN deals with its structural optimization involving the selection of preferred nodes (or FPNs) with specific local characteristics (such as the number of input variables, the order of the polynomial of the consequent part of fuzzy rules, and a collection of the specific subset of input variables) and addresses specific aspects of parametric optimization. Through the consecutive process of such structural and parametric optimization, an optimized and flexible fuzzy neural network is generated in a dynamic fashion. To evaluate the performance of the genetically optimized SOFPNN, the model is experimented with using two time series data(gas furnace and chaotic time series), A comparative analysis reveals that the proposed SOFPNN exhibits higher accuracy and superb predictive capability in comparison to some previous models available in the literatures.

Keywords

References

  1. V. Cherkassky, D. Gehring, F. Mulier, 'Comparison of adaptive methods for function estimation from samples', IEEE Trans. Neural Networks, Vol. 7, pp. 969 984, July, 1996 https://doi.org/10.1109/72.508939
  2. J. A. Dickerson and B. Ksoko, 'Fuzzy function approximation with ellipsoidal rules', IEEE Trans. Syst., Man, Cybernetics, Part B, Vol. 26, pp.542 560, Aug., 1996 https://doi.org/10.1109/3477.517030
  3. A. G. Ivakhnenko, 'Polynomial theory of complex systems', IEEE Trans. on System, Man and Cybernetics, Vol. SMC-1, pp. 364-378, 1971
  4. A. G. Ivakhnenko and H. R. Madala, 'Inductive Learning Algorithms for Complex Systems Modeling', CRC Press, Boca Raton, Fl, 1994
  5. S.-K. Oh, W. Pedrycz, 'The design of self-organizing Polynomial Neural Networks', Information Science, Vol. 141, pp. 237-258, 2002 https://doi.org/10.1016/S0020-0255(02)00175-5
  6. S.-K. Oh, W. Pedrycz and B.-J. Park, 'Polynomial Neural Networks Architecture: Analysis and Design', Computers and Electrical Engineering, Vol. 29, Issue 6, pp. 703-725, 2003 https://doi.org/10.1016/S0045-7906(02)00045-9
  7. C. W. Xu, and Y. Zailu, 'Fuzzy model identification self-learning for dynamic system', IEEE Trans. on Syst. man, Cybern., Vol. SMC-17, No.4, pp.683-689, 1987 https://doi.org/10.1109/TSMC.1987.289361
  8. W. Pedrycz, 'An identification algorithm in fuzzy relational system', Fuzzy Sets Syst., Vol. 13, pp.153-167, 1984 https://doi.org/10.1016/0165-0114(84)90015-0
  9. S.-K. Oh and W. Pedrycz, 'Fuzzy Polynomial Neuron-based Self-Organizing Neural Networks', Int. J. of General Systems, Vol. 32, No. 3, pp. 237-250, May, 2003 https://doi.org/10.1080/0308107031000090756
  10. S.-K. Oh, W. Pedrycz and T.-C. Ahn, 'Selforganizing neural networks with fuzzy polynomial neurons', Applied Soft Computing, Vol. 2, Issue 1F, pp. 1-10, Aug. 2002 https://doi.org/10.1016/S1568-4946(02)00023-6
  11. S.-K. Oh, W. Pedrycz, H.-S. Park, 'Self-organizing Networks in Modeling Experimental Data in Software Engineering', IEE Proc.-Computers and Digital Techniques, Vol. 149, Issue 3, pp. 61-78, May, 2002 https://doi.org/10.1049/ip-cdt:20020411
  12. S.-K. Oh and D.-Y. Lee, 'Advanced Self-organizing Neural Networks with Fuzzy Polynomial Neurons: Analysis and Design', KIEE International Transactions on Systems and Control(SC), Vol. 12D, No. 1, pp. 12-16, March, 2002
  13. Holland, J. H., Adaptation In Natural and Artificial Systems, The University of Michigan Press, Ann Arbour. 1975
  14. D. E. Goldberg, Optimization & Machine Learning,Genetic Algorithm in search, Addison wesley, 1989
  15. K. De Jong. Are genetic algorithms function optimizers? In Proc. of PPSN Ⅱ(Parallel Problem Solving from Nature), pages 3-13, Amsterdam, North Holland, 1992
  16. D. E. Box and G. M. Jenkins, Time Series Analysis, Forcasting and Control, California: Holden Day, 1976
  17. M. Sugeno and T. Yasukawa, 'Linguistic modeling based on numerical data', IFSA 91, Brussels, Computer, Management & Systems Science, pp. 264-267, 1991
  18. J. Q. Chen, Y. G. Xi and Z.J. Zhang, 'A clustering algorithm for fuzzy model identification', Fuzzy Sets and Systems, Vol. 98, pp. 319-329, 1998 https://doi.org/10.1016/S0165-0114(96)00384-3
  19. A. F. Gomez-Skarmeta, M. Delgado and M. A. Vila, 'About the use of fuzzy clustering techniques for fuzzy model identification', Fuzzy Sets and Systems, Vol. 106, pp. 179-188, 1999 https://doi.org/10.1016/S0165-0114(97)00276-5
  20. S.-K. Oh and W. Pedrycz, 'Identification of Fuzzy Systems by means of an Auto-Tuning Algorithm and Its Application to Nonlinear Systems', Fuzzy sets and Systems, Vol. 115, No. 2, pp. 205-230, 2000 https://doi.org/10.1016/S0165-0114(98)00174-2
  21. E.-T. Kim, et al, 'A new approach to fuzzy modeling', IEEE Trans. Fuzzy Systems', IEEE Trans. Fuzzy Systems, Vol. 5, No. 3, pp. 328-337, 1997 https://doi.org/10.1109/91.618271
  22. E.-T. Kim, et al, 'A simple identified Sugeno-type fuzzy model via double clustering', Infromation Science, Vol. 110, pp. 25-39, 1998 https://doi.org/10.1016/S0020-0255(97)10083-4
  23. J. Leski and E. Czogala, 'A new artificial neural networks based fuzzy inference system with moving consequents in if-then rules and selected applications', Fuzzy Sets and Systems, Vol. 108, pp. 289-297, 1999 https://doi.org/10.1016/S0165-0114(97)00314-X
  24. Y. Lin, G. A. Cunningham Ⅲ, 'A new approach to fuzzy-neural modeling', IEEE Trans. Fuzzy Systems, Vol. 3, No. 2, pp. 190-197, 1995 https://doi.org/10.1109/91.388173
  25. Yin Wang and Gang Rong, 'A self-organizing neural-network-based fuzzy system', Fuzzy Sets and Systems, Vol. 103, pp. 1-11, 1999 https://doi.org/10.1016/S0165-0114(97)00196-6
  26. H.-S. Park, S.-K. Oh, Y.-W. Yoon, 'A New Modeling Approach to Fuzzy-Neural Networks Architecture', Journal of Control, Automation and Systems Engineering, Vol. 7, No. 8, pp. 664-674
  27. S.-K. Oh, D.-W. Kim and B.-J. Park, 'A Study on the Optimal Design of Polynomial Neural Networks Structure', The Transactions of The Korean Institute of Electrical Engineers, Vol. 49D, No. 3, pp. 145-156
  28. S.-K. Oh, W. Pedrycz and D.-W. Kim, 'Hybrid Fuzzy Polynomial Neural Networks', Int. J. of Uncertainty, fuzziness and Knowledge-Based Systems, Vol. 10, No. 3, pp. 257-280, June, 2002 https://doi.org/10.1142/S0218488502001478
  29. L. X. Wang, J. M. Mendel, 'Generating fuzzy rules from numerical data with applications', IEEE Trans. Systems, Man, Cybern., Vol. 22, No. 6, pp. 1414-1427, 1992 https://doi.org/10.1109/21.199466
  30. J. S. R. Jang, 'ANFIS: Adaptive-Network-Based Fuzzy Inference System', IEEE Trans. System. Man. and Cybern., Vol. 23, No. 3, pp. 665-685, 1993 https://doi.org/10.1109/21.256541
  31. L. P. Maguire, B. Roche, T. M. McGinnity, L. J. McDaid, 'Predicting a chaotic time series using a fuzzy neural network', Information Sciences, Vol. 112, pp. 125-136, 1998 https://doi.org/10.1016/S0020-0255(98)10026-9
  32. C. James Li, T.-Y. Huang, 'Automatic structure and parameter training methods for modeling of mechanical systems by recurrent neural networks', Applied Mathematical Modeling, Vol. 23, pp. 933-944, 1999 https://doi.org/10.1016/S0307-904X(99)00020-7
  33. A. S. Lapedes and R. Farber, 'Nonlinear signal processing using neural networks: prediction and systems modeling', Technical Report LA-UR-87-2662, Los Alamos National Laboratory, Los Alamos, New mexico 87545, 1987
  34. 오성권, 'C 프로그래밍에 의한 퍼지모델 및 제어시스템', 내하출판사, 2002. 1
  35. 오성권, '프로그래밍에 의한 컴퓨터지능(퍼지, 신경회로망및 유전자알고리즘을 중심으로)', 내하출판사, 2002. 8