Sufficient conditions on uniform approximation of multivariate functions by general Takagi-Sugeno fuzzy systems with linear rule consequent

IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans.

Volumn 28, Issue 4, 1998, Pages 515-520

  Ying, Hao ^a  

^a UNIVERSITY OF TEXAS MEDICAL BRANCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; FUZZY CONTROL; LOGIC GATES; MATHEMATICAL MODELS; POLYNOMIALS; THEOREM PROVING;

LINEAR RULE CONSEQUENT; MULTIVARIATE FUNCTIONS; TAKAGI-SUGENO FUZZY SYSTEMS;

FUZZY SETS;

EID: 0032121932     PISSN: 10834427     EISSN: None     Source Type: Journal    
DOI: 10.1109/3468.686713     Document Type: Article

References (23)

1. S. Abe and M.-S. Lan, "Fuzzy rules extraction directly from numerical data for function approximation," IEEE Trans. Syst., Man, Cybern., vol. 25, pp. 119-129, 1995.
2. I. N. Bronshtein and K. A. Semendyayev, Handbook of Mathematics. New York: Van Nostrand Reinhold, 1985.
3. J. J. Buckley, "Sugeno type controllers are universal controllers," Fuzzy Sets Syst., vol. 53, pp. 299-303, 1993.
4. J. L. Castro and M. Delgado, "Fuzzy systems with defuzzification are universal approximators," IEEE Trans. Syst., Man, Cybern., vol. 26, pp. 149-152, 1996.
5. J. A. Dickerson and B. Kosko, "Fuzzy function approximation with ellipsoidal rules," IEEE Trans. Syst., Man, Cybern., vol. 26, pp. 542-560, 1996.
6. D. P. Filev and R. R. Yager, "A generalized defuzzification method via BAD distributions," Int. J. Intell. Syst., vol. 6, pp. 687-697, 1991.
7. V. Gorrini, T. Salome, and H. Bersini, "Self-structuring fuzzy systems for function approximation," in Proc. 1995 IEEE Int. Conf. Fuzzy Systems, Yokohama, Japan, Mar. 1995, pp. 919-926.
8. M. M. Gupta and J. Qi, "Theory of T-norms and fuzzy inference methods," Fuzzy Sets Syst., vol. 40, pp. 431-450, 1991.
9. _, "Design of fuzzy logic controllers based on generalized T-operators," Fuzzy Sets Syst., vol. 40, pp. 473-490, 1991.
10. B. Kosko, "Fuzzy systems as universal approximators," in Proc. IEEE Int. Conf. Fuzzy Systems, San Diego, CA., Mar. 8-12, 1992.
11. E. G. Laukonen and K. M. Passino, "Fuzzy systems for function approximation with applications to failure estimation," in Proc. 1994 IEEE Int. Symp. Intelligent Control, Columbus, OH, Aug. 1994, pp. 184-189.
12. F. L. Lewis, S.-Q. Zhu, and K. Liu, "Function approximation by fuzzy systems," in Proc. 1995 American Control Conf., Seattle, WA, June 1995, pp. 3760-3764.
13. H. T. Nguyen, V. Kreinovich, and O. Sirisaengtaksin, "Fuzzy control as a universal control tool," Fuzzy Sets Syst., vol. 80, pp. 71-86, 1996.
14. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Syst., Man, Cybern., vol. 15, pp. 116-132, 1985.
15. L.-X. Wang, "Fuzzy systems are universal approximators," in Proc. IEEE Int. Conf. Fuzzy Systems, San Diego, CA., Mar. 8-12, 1992.
16. L.-X. Wang and J. M. Mendel, "Fuzzy basis functions, universal approximation, and orthogonal least-squares learning," IEEE Trans. Neural Networks, vol. 3, pp. 807-814, 1992.
17. H. Ying, "Sufficient conditions on general fuzzy systems as function approximators," Automatica, vol. 30, pp. 521-525, 1994.
18. H. Ying and G.-R. Chen, "Necessary conditions for some typical fuzzy systems as universal approximators," Automatica, vol. 33, pp. 1333-1338, 1997.
19. H. Ying, "The Takagi-Sugeno fuzzy controllers using the simplified linear control rules are nonlinear variable gain controllers," Automatica, vol. 34, no. 2, pp. 157-167, 1998.
20. _, "Constructing nonlinear variable gain controllers via the Takagi-Sugeno fuzzy control," IEEE Trans. Fuzzy Syst., vol. 6, no. 2, pp. 226-234, 1998.
21. H. Ying, Y.-S. Ding, S.-K. Li, and S.-H. Shao, "Comparison of necessary conditions for typical Takagi-Sugeno and Mamdani fuzzy systems as universal approximators," submitted for publication.
22. X.-J. Zeng and M. G. Singh, "Approximation theory of fuzzy systems - MIMO case," IEEE Trans. Fuzzy Syst., vol. 3, pp. 219-235, 1995.
23. _, "Approximation accuracy analysis of fuzzy systems as function approximators," IEEE Trans. Fuzzy Syst., vol. 4, pp. 44-63, 1996.