Monotonic fuzzy systems as universal approximators for monotonic functions

Intelligent Automation and Soft Computing

Volumn 18, Issue 1, 2012, Pages 13-31

  Kim, Jinwook ^a   Won, Jin Myung ^b   Koo, Kyungmo ^c   Lee, Jin S ^a  

^a Pohang University of Science and Technology (POSTECH)   (South Korea)

^b UNIVERSITY OF WATERLOO   (Canada)

^c Samsung Electro Mechanics   (South Korea)

Author keywords

Fuzzy constraint satisfaction; Fuzzy systems; Monotonic fuzzy systems; Monotonicity constraints; Universal approximation

Indexed keywords

EID: 84862520893     PISSN: 10798587     EISSN: 2326005X     Source Type: Journal    
DOI: 10.1080/10798587.2012.10643224     Document Type: Article

References (31)

1. C.J. Wu and A.H. Sung, “A general purpose fuzzy controller for monotone functions,” IEEE Trans. Syst. Man Cybern. B, Cybern., vol. 26, no. 5, pp. 803-808, 1996.
2. C.J. Wu, “Guaranteed accurate fuzzy controllers for monotone-functions,” Fuzzy Sets Syst., vol 92, no. 1, pp. 71-82, 1997.
3. P. Lindeskog and L. Ljung, “Ensuring monotonic gain characteristics in estimated models by fuzzy model structures,” Automatica, vol. 36, no. 2, pp. 311-317, 2000.
4. H. Zhao and C. Zhu, “Monotone fuzzy control method and its control performance,” in Proc. 2000 IEEE Int. Conf. Syst. Man and Cybern., Nashville, TN, 2000, pp. 3740-3745.
5. V.S. Kouikoglou and Y.A. Phillis, “On the monotonicity of hierarchical sum-product fuzzy systems,” Fuzzy Sets Syst., vol. 160, pp. 3530-3538, 2009.
6. J. M. Won, K. Seo, S. K. Hwang, and J. S. Lee, “Evolutionary computation based identification of a monotonic Takagi-Sugeno-Kang fuzzy system,” in Proc. 2001 IEEE Intern. Conf. Fuzzy Systems, Melbourne, Australia, 2001.
7. K. Koo, J.M. Won, and J.S. Lee, “Least squares identification of monotonic fuzzy systems,” in Proc. NAFIPS-2004, Banff, Alberta, Canada, 2004.
8. S.Y. Park, J.S. Lee, J.-Y. Choi, and B.H. Park, “Automatic current control of magnet cranes for steel plate yard automation,” Control Engineering Practice, vol. 6, no. 10, pp. 1193-1208, 1998.
9. J.M. Won, S.Y. Park and J.S. Lee, “Parameter conditions for monotonic Takagi-Sugeno-Kang fuzzy system,” Fuzzy Sets Syst., vol. 132, no. 2, pp. 135-146, 2002.
10. L.X. Wang, A Course in Fuzzy Systems and Control, Englewood Cliffs, NJ: Prentice-Hall, 1997.
11. L.X. Wang and J.M. Mendel, “Fuzzy basis functions, universal approximation, and orthogonal least square learning,” IEEE trans. Neural Netw., vol. 3, no. 5, pp. 807-814, 1992.
12. J.J. Buckley, “Sugeno type controllers are universal controllers,” Fuzzy Sets Syst., vol. 53, no. 3, pp. 299-303, 1993.
13. J.L. Castro and M. Delgado, “Fuzzy systems with defuzzification are universal approximators,” IEEE Trans. Syst. Man Cybern. B, Cybern., vol. 26, no. 1, pp. 149-152, 1996.
14. B. Kosko, “Fuzzy systems as universal approximators,” in Proc. IEEE Int. Conf. Fuzzy Syst., San Diego, CA, 1992, pp. 8-12.
15. F.L. Lewis, S.-Q. Zhu, and K. Liu, “Function approximation by fuzzy systems,” in Proc. 1995 American Control Conf., Seattle, WA, 1995, pp. 3760-3764.
16. H.T. Nguyen, V. Kreinovich, and O. Sirisaengtaksin, “Fuzzy control as a universal control tool,” Fuzzy Sets Syst., vol. 80, no. 1, pp. 71-86, 1996.
17. L.-X. Wang, “Fuzzy systems are universal approximators,” in Proc. IEEE Int. Conf. Fuzzy Syst., San Diego, CA, 1992, pp. 1163-1170.
18. H. Ying, “Sufficient conditions on general fuzzy systems as function approximators,” Automatica, vol. 30, no. 3, pp. 521-525, 1994.
19. H. Ying and G.-R. Chen, “Necessary conditions for some typical fuzzy systems as universal approximators,” Automatica, vol. 33, no. 7, pp. 1333-1338, 1997.
20. 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, 1998.
21. 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, 1994.
22. 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, 1995.
23. V. Kreinovich, H.T. Nguyen, and Y. Yam, “Fuzzy systems are universal approximators for a smooth function and its derivative,” Int. J. Intell. Syst., vol. 15, no. 6, pp. 565-574, 2000.
24. L.X. Wang, “Universal approximation by hierarchical fuzzy systems,” Fuzzy Sets Syst., vol. 93, pp. 223-230, 1998.
25. C. Wei, L.X. Wang, “A note on universal approximation by hierarchical fuzzy systems,” Information Sciences, vol. 123, pp. 241-248, 2000.
26. M.G. Joo and J.S. Lee, “Hierarchical fuzzy logic scheme with constraints on the fuzzy rule,” Intelligent Automation and Soft Computing, vol. 7, no. 4, pp. 259-271, 2001.
27. M.G. Joo and J.S. Lee, “A class of hierarchical fuzzy system with constraints on the fuzzy rule,” IEEE Trans. Fuzzy Syst., vol. 13, no. 2, pp. 194-203, 2005.
28. P. Liu and H. Li, “Hierarchical TS fuzzy system and its universal approximation,” Information Sciences, vol. 169, pp. 279-303, 2005.
29. G.E.P. Box and G.M. Jenkins, Time series analysis, forecasting and control, Holden Day, San Francisco, 1970.
30. S.L. Chiu, “Selecting input variables for fuzzy models,” Int. J. Intell. Fuzzy Syst., vol. 4, no. 4, pp. 243-256, 1996.
31. J. Hubbard and B. Burke Hubbard, Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, Prentice Hall, 2002.