Sufficient conditions to impose derivative constraints on MISO Takagi-Sugeno fuzzy logic systems

IEEE Transactions on Fuzzy Systems

Volumn 13, Issue 4, 2005, Pages 454-467

  Mencattini, Arianna ^a   Salmeri, Marcello ^a   Salsano, Adelio ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Derivative constraints; Function approximation and interpolation; Fuzzy logic systems (FLSs); Sufficient conditions; Uniform approximation

Indexed keywords

APPROXIMATION THEORY; INTERPOLATION; MATHEMATICAL MODELS; OPTIMIZATION; POLYNOMIALS; THEOREM PROVING;

DERIVATIVE CONSTRAINTS; FUZZY LOGIC SYSTEMS (FLSS); MULTIPLE INPUT SINGLE OUTPUT (MISO); SUFFICIENT CONDITIONS; UNIFORM APPROXIMATION;

FUZZY SETS;

EID: 26944486289     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2004.841742     Document Type: Article

References (41)

1. T. J. Rivlin, An Introduction to the Approximation of Functions. New York: Dover, 1981.
2. M. J. D. Powell, Approximation Theory and Methods. Cambridge, MA: Cambridge Univ. Press, 1981.
3. M. Salmeri, A. Mencattini, S. Bertazzoni, D. Di Giovenale, and A. Salsano, "High spectral purity digital direct synthesizer implementation by means of a fuzzy approximator," Appl. Soft Comput. J., Special Issue Hardware Implementations of Soft Computing Techniques, vol. 4, no. 3, pp. 241-257, Aug. 2004.
4. G. Leuzzi, A. Mencattini, and M. Salmeri, "Physics-based correction of extracted conductance parameters of nonlinear microwave semiconductor devices," J. Comput. Electron., vol. 2, no. 2-4, pp. 363-368, Dec. 2003.
5. X.-J. Zeng and M. G. Singh, "Approximation theory of fuzzy systems - SISO case," IEEE Trans. Fuzzy Syst., vol. 2, no. 2, pp. 162-176, Apr. 1994.
6. X.-J. Zeng and M. G. Singh, "Approximation theory of fuzzy systems - MIMO case," IEEE Trans. Fuzzy Syst., vol. 3, no. 2, pp. 219-235, Apr. 1995.
7. X.-J. Zeng and M. G. Singh, "Approximation accuracy analysis of fuzzy systems as function approximators," IEEE Trans. Fuzzy Syst., vo. 4, no. 1, pp. 44-63, Feb. 1996.
8. V. Kreinovich, H. T. Nguyen, and Y. Yam, "Fuzzy systems are universal approximators for a smooth function and its derivatives," Int. J. Intell. Syst., vol. 15, pp. 565-574, 2000.
9. M. Landajo, M. J. Rìo, R. Pérez, and A. 2001, "A note on smooth approximation capabilities of fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 9, no. 2, pp. 229-237, Apr. 2001.
10. R. Hassine, F. Karray, A. M. Alimi, and M. Selmi, "Approximation properties of fuzzy systems for smooth functions and their first-order derivative," IEEE Trans. Syst., Man, Cybern. A, Syst. Humans, vol. 33, no. 2, pp. 160-168, Mar. 2003.
11. H. Ying, "General Takagi-Sugeno fuzzy systems are universal approximators," in Proc. IEEE Int. Conf. Fuzzy Systems, vol. 1, Anchorage, AK, May 1998, pp. 819-823.
12. H. Ying and G. Chen, "Necessary conditions for some typical fuzzy systems as universal approximators," Automatica, vol. 33, no. 7, pp. 1333-1338, Jul. 1997.
13. H. Ying, "Sufficient conditions on uniform approximation of multivariate functions by general Takagi-Sugeno fuzzy systems with linear rule consequent," IEEE Trans. Syst., Man, Cybern. A, Syst. Humans, vol. 28, no. 4, pp. 515-520, Jul. 1998.
14. H. Ying, Y. Ding, S. Li, and S. Shao, "Typical Takagi-Sugeno and Mamdani fuzzy systems as universal approximators: Necessary conditions and comparison," in Proc. IEEE Int. Conf. Fuzzy Syst., vol. 1, Anchorage, AK, May 1998, pp. 824-828.
15. H. Ying, Y. Ding, S. Li, and S. Shao, "Comparison of necessary conditions for typical Takagi-Sugeno and Mamdani fuzzy systems as universal approximators," IEEE Trans. Syst., Man, Cybern. A, Syst. Humans, vol. 29, no. 4, pp. 508-514, Aug. 1999.
16. Y. Ding, H. Ying, and S. Shao, "Necessary conditions on minimal system configuration for general MISO Mamdani fuzzy systems as universal approximators," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 30, no. 6, pp. 857-864, Dec. 2000.
17. K. Zeng, N. Y. Zhang, and W. L. Xu, "A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 8, no. 6, pp. 773-780, Dec. 2000.
18. D. Lisin and M. A. Gennert, "Optimal function approximation using fuzzy rules," in Proc. IEEE Int. Conf. North American Fuzzy Information Processing Soc., New York, Jun. 10-12, 1999, pp. 184-188.
19. A. Fiordaliso, "Autostructuration of fuzzy systems by rules sensitivity analysis," Fuzzy Sets Syst., vol. 118, no. 2, pp. 281-296, Mar. 2001.
20. L.-X. Wang and J. M. Mendel, "Fuzzy basis functions, universal approximation, and orthogonal least-squares learning," IEEE Trans. Neural Networks, vol. 3, no. 5, pp. 807-814, Sep. 1992.
21. H. M. Kim and J. M. Mendel, "Fuzzy basis functions: Comparison with other basis functions," IEEE Trans. Fuzzy Syst., vol. 3, no. 2, pp. 158-168, Apr. 1995.
22. X.-J. Zeng and M. G. Sing, "A relationship between membership functions and approximation accuracy in fuzzy systems," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 26, no. 1, pp. 176-180, Feb. 1996.
23. S. Mitaim and B. Kosko, "What is the best shape for a fuzzy set in function approximation?," in Proc. IEEE Int. Conf. Fuzzy Systems, vol. 2, New Orleans, LA, 1996, pp. 1237-1243.
24. J. A. Dickerson and B. Kosko, "Fuzzy function approximation with ellipsoidal rules," IEEE Trans. Syst., Man, Cybern. B, Cybern, vol. 26, no. 4, pp. 542-560, Aug. 1996.
25. Z.-H. Mao, Y.-D Li, and X.-F. Zhang, "Approximation capability of fuzzy systems using translations and dilatations of one fixed function as membership functions," IEEE Trans. Fuzzy Syst., vol. 5, no. 4, pp. 468-473, Aug. 1997.
26. S. Nejim, "Optimal approximation of functions using piecewise polynomial fuzzy systems," in Proc. IEEE Int. Conf. North American Fuzzy Information Processing Soc., New York, Jun. 10-12, 1999, pp. 193-197.
27. T. A. Runkler and J. C. Bezdek, "Function approximation with polynomial membership functions and alternating cluster estimation," Fuzzy Sets Syst., vol. 101, no. 2, pp. 207-218, Jan. 1999.
28. S. Mitaim and B. Kosko, "The shape of fuzzy sets in adaptive function approximation," IEEE Trans. Fuzzy Syst., vol. 9, no. 4, pp. 637-656, Aug. 2001.
29. L.-W. Chan, "The interpolation property of fuzzy polinomial approximation" in Proc. IEEE Int. Symp. Speech, Image Processing and Neural Networks, vol. 2, Hong Kong, Apr. 13-16, 1994, pp. 449-452.
30. X.-J. Zeng and M. G. Singh, "Approximation properties of fuzzy systems generated by the min inference," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 26, no. 1, pp. 187-193, Feb. 1996.
31. S. Mitaim and B. Kosko, "Adaptive joint fuzzy sets for function approximarion," in Proc. IEEE Int. Conf. Neural Networks, vol. 1, Houston, TX, Jun. 9-12, 1997, pp. 537-542.
32. F. Ashrafzadeh, E. P. Nowicki, M. Mohamadian, and J. C. Salmon, "Optimal approximation of nonlinear functions by fuzzy systems," in Proc. IEEE Canadian Conf. Electrical and Computer Engineering, Engineering Innovation: Voyage of Discovery, vol. 2, St. John's, Newfoundland, Canada, May 1997, pp. 781-784.
33. L.-X. Wang, "Universal approximation by hierarchical fuzzy systems," Fuzzy Sets Syst., vol. 93, no. 2, pp. 223-230, Jan. 1998.
34. M. Salmeri, A. Mencattini, and R. Rovatti, "Function approximation using nonnormalized SISO fuzzy systems," Int. J. Approx. Reason., vol. 26, no. 3, pp. 211-231, Apr. 2001.
35. A. Sala and P. Albertos, "Inference error minimization: Fuzzy modeling of ambiguous functions," Fuzzy Sets Syst., vol. 121, no. 1, pp. 95-111, Jul. 2001.
36. I. Elbadawi, A. R. Gallant, and G. Souza, "An elasticity can be estimated consistently without a priory knowledge of functional form," Econometrica, vol. 51, no. 6, pp. 1731-1751, Nov. 1983.
37. D.K. Andrews, "Asymptotic normality of series estimators for nopparametric and semiparametric regression models," Econometrica, vol. 59, no. 2, pp. 307-345, Mar. 1991.
38. M. Jordan, "Generic constraints on underspecified target trajectories," in Proc. Int. Joint Conf. Neural Networks, vol. 1, Piscataway, NJ, 1989, pp. 217-225.
39. W. Pedrycz, "Why triangular membership functions?" Fuzzy Sets Syst., vol. 64, no. 1, pp. 21-30, 1994.
40. D. P. Filev and R. R. Yager, "A generalized defuzzification method via BAD distribution," Int. J. Intell. Syst., vol. 6, pp. 687-697, 1991.
41. R. Rovatti, "Fuzzy piecewise multilinear and piecewise linear systems as universal approximators in sobolev norms," IEEE Trans. Fuzzy Syst., vol. 6, no. 2, pp. 235-249, Apr. 1998.