A class of hierarchical fuzzy systems with constraints on the fuzzy rules

IEEE Transactions on Fuzzy Systems

Volumn 13, Issue 2, 2005, Pages 194-203

  Joo, Moon G ^a   Lee, Jin S ^b  

^a Pukyong National University   (South Korea)

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

Author keywords

Fuzzy control; Hierarchical fuzzy logic system; Stone Weierstrass theorem; Univeral approximation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; FUZZY SETS; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS; THEOREM PROVING;

HIERARCHICAL FUZZY LOGIC SYSTEM; STONE-WEIERSTRASS THEOREM; UNIVERSAL APPROXIMATION;

FUZZY CONTROL;

EID: 17644369993     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2004.840096     Document Type: Article

References (24)

1. G. V. S. Raju, J. Zhou, and R. A. Kisner, "Hierarchical fuzzy control," Int. J. Control, vol. 54, pp. 1201-1216, 1991.
2. G. V. S. Raju and J. Zhou, " Adaptive hierarchical fuzzy controller," IEEE Trans. Syst., Man, Cybern., vol. 23, no. 4, pp. 973-980, Jul./Aug. 1993.
3. M. G. Joo and J. S. Lee, "Hierarchical fuzzy logic scheme with constraints on the fuzzy rule," Int. J. Intell. Autom. Soft Comput. vol. 7, no. 4, pp. 259-271, 2001.
4. M. G. Joo and J. S. Lee, "Universal approximation by hierarchical fuzzy system with constraints on the fuzzy rule," Fuzzy Sets Syst., vol. 130, no. 2, pp. 175-188, 2002.
5. H. Kikuchi, A. Otake, and S. Nakanishi, "Functional completness of hierarchical fuzzy modeling," Inf. Sci., vol. 110, pp. 51-60, 1998.
6. H. Kikuchi and N. Takagi, "Hierachical fuzzy modeling and jointly expandable functions," Int. J. Intell. Syst., vol. 17, pp. 515-529, 2002.
7. L.-X. Wang, "Universal approximation by hierarchical fuzzy systems," Fuzzy Sets Syst., vol. 93, pp. 223-230, 1998.
8. L.-X. Wang, "Analysis and design of hierarchical fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 7, no. 5, pp. 617-624, Oct. 1999.
9. C. Wei and L.-X. Wang, "A note on universal approximation by hierarchical fuzzy systems," Inf. Sci., vol. 123, pp. 241-248, 2000.
10. O. Huwendiek and W. Brockmann, "NetFAN - A structured adaptive fuzzy approach," in Proc. IEEE Int. Conf. Neural Networks, 1996, pp. 1079-1084.
11. O. Huwendiek and W. Brockmann, "On the applicablility of the NetFAN-approach to function approximation," in Proc. IEEE Int. Conf. Fuzzy Syst., 1997, pp. 477-482.
12. O. Huwendiek and W. Brockmann, "Function approximation with decomposed fuzzy systems," Fuzzy Sets Syst., vol. 101, pp. 273-286, 1999.
13. W. Rudin, Principles of Mathematical Analysis. New York: McGraw-Hill, 1976.
14. F.-l. Chung, J.-c. Duan, and D. S. Yeung, "Deriving multistage FNN models from Takagi and Sugeno's fuzzy systems," in Proc. IEEE Int. Conf. Fuzzy Syst., 1998, pp. 1259-1264.
15. R. Holve, "Investigation of automatic role generation for hierarchical fuzzy systems," IEEE Trans. Syst., Man, Cybern., vol. 29, no. 1, ,pp. 98-109, Jan. 1999.
16. D. A. Linkens and H. O. Nyongesa, "A hierarchical multivariable fuzzy controller for learning with genetic algorithms," Int. J. Control vol. 63, pp. 865-883, 1996.
17. K. Shimojima, T. Fukuda, and Y. Hasegawa, "Self-tuning fuzzy modeling with adaptive membership function, roles, and hierarchical structure based on genetic algorithm," Fuzzy Sets Syst., vol. 71, pp. 295-309, 1995.
18. T. Fukuda, Y. Hasegawa, and K. Shimojima, "Structure organization of hierarchical fuzzy model using by genetic algorithm," in IEEE Int. Conf. Fuzzy Systems, vol. 1, 1995, pp. 295-300.
19. T. Furuhashi, S. Matsushita, H. Tsutsui, and Y. Uchikawa, "Knowledge extraction from hierarchical fuzzy model obtained by fuzzy neural networks and genetic algorithm," in Proc. Int. Conf. Neural Networks vol. 4, 1997, pp. 2374-2379.
20. K. Tachibana and T. Furuhashi, "Uneven allocation of membership functions for hierarchical fuzzy modeling using genetic algorithm, in Proc. IEEE Int. Conf. Evolutionary Computation, 1998, pp. 746-751.
21. L.-X. Wang, A Course in Fuzzy Systems and Control. Upper Saddle River, NJ: Prentice-Hall, 1997.
22. J. J. Buckley and Y. Hayashi, "Fuzzy input-output controllers are universal approximators," Fuzzy Sets Syst., vol. 58, pp. 273-278, 1993.
23. K. Zeng, N.-Y. Zhang, and W.-L. Xu, "A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators," IEEE Trans. Fuzzy Syst., vol. 8, no. 6, pp. 773-780, Dec. 2000.
24. Hauser, J. S. Sastry, and P. Kokotovic, "Nonlinear control via approximate input-output linearization: The ball and beam example," IEEE Trans. Autom. Control, vol. 37, no. 3, pp. 392-398, Mar. 1992.