Fuzzy Optimization and Decision Making

, Volume 3, Issue 3, pp 195–216 | Cite as

Robust Adaptive Identification of Fuzzy Systems with Uncertain Data

  • Mohit Kumar
  • Regina Stoll
  • Norbert Stoll


This study presents a method of adaptive identification of parameters describing Sugeno fuzzy inference system in presence of bounded disturbances while maintaining the readability and interpretability of the fuzzy model during and after identification. This method do not require any a priori knowledge of a bound on the disturbance and noise and of a bound on the unknown parameters values. The method can be used for the robust and adaptive identification of slowly time varying nonlinear systems using fuzzy inference systems. The suggested method was used to build a fuzzy expert system that approximates the functional relationship between physical fitness and some of the measurable physiological parameters by their real measurements and opinion (human-experiences) of a medical expert.

fuzzy-modelling identification robustness nonlinear least squares 


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  1. Babuska, R. (2000). “Construction of Fuzzy Systems-interplay between Precision and Transparency,” In Proc. ESIT 2000, Aachen, pp. 445–452.Google Scholar
  2. Bodenhofer, U. and P. Bauer. (2000). “Towards an Axiomatic Treatment of Inter-Pretability,” In Proc. IIZUKA2000, Iizuka, pp. 334–339.Google Scholar
  3. 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(2002), 319–344.Google Scholar
  4. 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 2000.Google Scholar
  5. Hassibi, B., Ali H. Sayed, and Thomas Kailath. (1996). “H1 Optimality of the LMS Algorithms'', IEEE Transactions on Signal Processing 44(2), 267–280.CrossRefGoogle Scholar
  6. Ioannou, P. A. and J. Sun. (1996). “Robust Adaptive Control'', Prentic-Hall, Englewood Cliffs, NJ . Google Scholar
  7. Jang, J.-S. Roger. (1993). “ANFIS: Adaptive-network-based Fuzzy Inference Systems,” IEEE Trans.Syst. Man Cybern, 23(3), 665–685.CrossRefGoogle Scholar
  8. Lawson, C. L. and R. J. Hanson. (1995). “Solving Least Squares Problems'', SIAM Publications, Philadelphia . Google Scholar
  9. Mathelin, M. de. and R. Lozano. (1997). “Robust Adaptive Identification of Slowly Time Varying Parameters with Bounded Disturbances,” In Proc. ECC97, Brussels.Google Scholar
  10. Nauck, D. and R. Kruse. (1997). “Function Approximation by NEFPROX,” Proc. Second European Workshop on Fuzzy Decision Analysis and Neural Networks for Management, Planning and Optimization (EFDAN'97) Dortmund, pp. 160–169.Google Scholar
  11. Nauck, D. and R. Kruse. (1998). “A Neuro-Fuzzy Approach to Obtain Interpretable Fuzzy Systems for Function Approximation,” Proc. IEEE International Conference on Fuzzy Systems, 1998 (FUZZIEEE' 98), Anchorage, AK, May 4-9, pp. 1106–1111.Google Scholar
  12. Nauck, D. and R. Kruse. (1999). “Obtaining Interpretable Fuzzy Classification Rules from Medical Data,” Artificial Intelligence in Medicine, 16:149–169.CrossRefGoogle Scholar
  13. 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.CrossRefGoogle Scholar
  14. 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
  15. Tan, G. V. and X. Hu. (1996). “On Designing Fuzzy Controllers Using Genetic Algorithms,” In Proc. Fuzz-IEEE96 volume II, 905–911.Google Scholar
  16. 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, May 4-9, Anchorage, Alaska, USA, 797–802.Google Scholar
  17. 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

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Mohit Kumar
    • 1
  • Regina Stoll
    • 2
  • Norbert Stoll
    • 3
  1. 1.University of RostockRostockGermany
  2. 2.Institute of Occupational and Social Medicine, Faculty of MedicineUniversity of RostockRostockGermany
  3. 3.Institute of Automation, Department of Electrical Engineering and Information TechnologyUniversity of RostockRostock-WarnemndeGermany

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