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Fuzzy Optimization and Decision Making

, Volume 2, Issue 4, pp 317–336 | Cite as

Regularized Adaptation of Fuzzy Inference Systems. Modelling the Opinion of a Medical Expert about Physical Fitness: An Application

  • Mohit Kumar
  • Regina Stoll
  • Norbert Stoll
Article

Abstract

This study presents a new approach to adaptation of Sugeno type fuzzy inference systems using regularization, since regularization improves the robustness of standard parameter estimation algorithms leading to stable fuzzy approximation. The proposed method can be used for modelling, identification and control of physical processes. A recursive method for on-line identification of fuzzy parameters employing Tikhonov regularization is suggested. The power of approach was shown by applying it to the modelling, identification, and adaptive control problems of dynamic processes. The proposed approach was used for modelling of human-decisions (experience) with a fuzzy inference system and for the fuzzy approximation of physical fitness with real world medical data.

fuzzy approximation model identification ill-posed regularization nonlinear least squares inverse control generalized predictive control 

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References

  1. Babuska, R. (2000). “Construction of Fuzzy Systems-Interplay Between Precision and Transparency,” In Proc. ESIT 2000. Aachen, 445–452.Google Scholar
  2. Binder, A., H. W. Engl, C. W. Groetsch, A. Neubauer, and O. Scherzer. (1994). “Weakly Closed Nonlinear Operators and Parameter Identification in Parabolic Equations by Tikhonov Regularization,” Appl. Anal. 55, 215–234.Google Scholar
  3. Bodenhofer, U. and P. Bauer. (2000). “Towards an Axiomatic Treatment of Interpretability,” In Proc. IIZUKA2000. Iizuka, 334–339 (October).Google Scholar
  4. Burger, M., J. Haslinger and U. Bodenhofer. (2000). “Regularized Optimization of Fuzzy Controllers,” Technical Report SCCH-TR-0056, Software Competence Center Hagenberg.Google Scholar
  5. Burger, M., H. W. Engl, J. Haslinger, and U. Bodenhofer. (2002). “Regularized Data-Driven Construction of Fuzzy Controllers,” J. Inverse and Ill-posed Problems 10, 319–344.Google Scholar
  6. Engl, H. W., K. Kunisch, and A. Neubauer. (1989). “Convergence Rates for Tikhonov Regularization of Nonlinear Ill-Posed Problems” Inverse Problems 5, 523–540.Google Scholar
  7. Engl, H. W., M. Hanke, and A. Neubauer. (1996). Regularization of Inverse Problems. Dordrecht: Kluwer Academic Publishers.Google Scholar
  8. Espinosa, J. and J. Vandewalle. (2000). “Constructing Fuzzy Models with Linguistic Integrity from Numerical Data-AFRELI Algorithm,” IEEE Trans. Fuzzy Systems 8(5), 591–600 (October).Google Scholar
  9. Jang, J.-S. R., C.-T. Sun and E. Mizutani. (1997). Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence. Prentice Hall, Chapter 12, 345–360.Google Scholar
  10. Lawson, C. L. and R. J. Hanson. (1995). Solving Least squares Problems. Philadelphia: SIAM Publications.Google Scholar
  11. Nauck, D. and R. Kruse. (1999). “Obtaining Interpretable Fuzzy Classification Rules from Medical Data,” Artificial Intelligence in Medicine 16, 149–169.Google Scholar
  12. Setnes, M., R. Babuka, and H. B. Verbruggen. (1998). “Rule-Based Modeling: Precision and Transparency,” IEEE Trans. Syst. Man Cybern. Part C: Applications and Reviews 28, 165–69.Google Scholar
  13. Takagi, T. and M. Sugeno. (1985). “Fuzzy Identification of Systems and Its Applications to Modeling and Control,” IEEE Trans. Syst. Man Cybern 15(1), 116–132.Google Scholar
  14. Väinämö, K., S. Nissilä, T. Mäkikallio, M. Tulppo and J. Röning. (1996). “Artificial Neural Network for Aerobic Fitness Approximation,” International Conference on Neural Networks (ICNN96). Washington DC, USA (June 3- 6).Google Scholar
  15. Väinämö, K., T. Mäkikallio, M. Tulppo and J. Röning. (1998). “A Neuro-Fuzzy Approach to Aerobic Fitness Classification: A Multistructure Solution to the Context-Sensitive Feature Selection Problem], ” Proc. WCCI ‘98. Anchorage, Alaska, USA, 797–802 (May 4- 9).Google Scholar
  16. Widrow, B. and M. A. Lehr. (1990). “30 Years of Adaptive Neural Networks: Perceptron, Madline and Backpropagation,” Proceeding of the IEEE 78(9), 1415–1422.Google Scholar
  17. Zadeh, L. A. (1973). “Outline of a New Approach to the Analysis of Complex Systems and Decision Processes,” IEEE Trans. Syst. Man Cybern 3(1), 28–44.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Mohit Kumar
    • 1
  • Regina Stoll
    • 1
  • Norbert Stoll
    • 2
  1. 1.Institute of Occupational and Social Medicine, Faculty of MedicineUniversity of RostockRostockGermany
  2. 2.Institute of Automation, Department of Electrical Engineering and Information TechnologyUniversity of RostockRostock-WarnemndeGermany

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