Hierarchical fuzzy systems for function approximation on discrete input spaces with application

IEEE Transactions on Fuzzy Systems

Volumn 16, Issue 5, 2008, Pages 1197-1215

  Zeng, Xiao Jun ^a   Goulermas, John Yannis ^b   Liatsis, Panos ^c   Wang, Di ^d   Keane, John A ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b UNIVERSITY OF LIVERPOOL   (United Kingdom)

^c CITY UNIVERSITY   (United Kingdom)

^d ThinkAnalytics Ltd   (United Kingdom)

Author keywords

Discrete spaces; Function approximation; Hierarchical fuzzy systems; Kolmogorov's theorem; Site selection decision support; Universal Approximation

Indexed keywords

CONTROL THEORY; DECISION SUPPORT SYSTEMS; FUZZY CONTROL; FUZZY NEURAL NETWORKS; FUZZY SYSTEMS; HIERARCHICAL SYSTEMS; KNOWLEDGE BASED SYSTEMS; NETWORK PROTOCOLS; NEURAL NETWORKS; POLYNOMIAL APPROXIMATION; PROBABILITY DENSITY FUNCTION; SENSOR NETWORKS; SITE SELECTION; VEGETATION;

DISCRETE SPACES; FUNCTION APPROXIMATION; HIERARCHICAL FUZZY SYSTEMS; KOLMOGOROV'S THEOREM; SITE SELECTION DECISION SUPPORT; UNIVERSAL APPROXIMATION;

FUZZY LOGIC;

EID: 54349119610     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2008.924343     Document Type: Article

References (40)

1. J. Abonyi, R. Babuska, and F. Szeifert, "Modified Gath-Geva fuzzy clustering for identification of Takagi-Sugeno fuzzy models," IEEE Trans. Syst., Man., Cybern. - B, vol. 32, no. 5, pp. 612-621, Oct. 2002.
2. J. J. Buckley, "Universal fuzzy controllers," Automatica, vol. 28, pp. 1245-1248, 1992.
3. R. Babuska. (2002, Feb.). Fuzzy systems, modeling and identification [Online]. Available: http://www.dcsc.tudelft.nl/ ~babuska/transp/fuzzmod.pdf
4. R. L. David, "Evaluation of retail store attributes and sales performance," Eur. J. Marketing, vol. 7, pp. 89-102, 1973.
5. R. J. P. de Figueiredo, "Implications and applications of Kolmogorov's superposition theorem," IEEE Trans. Autom. Control., vol. 25, no. 6, pp. 1227-1231, Dec. 1980.
6. M. M. Fischer and M. Reismann, "A methodology for neural spatial interaction modeling," Geograph. Anal., vol. 34, pp. 93-111, 2002.
7. A. Ghosh and S. L. McLafferty, Location Strategies for Retail and Service Firms. Toronto, ON, Canada: D.C. Heath and Company, 1987.
8. T. Hernandez and D. Bennison, "The art and science of retail location decisions," Int. J. Retail Distrib. Manage., vol. 28, no. 8, pp. 357-367, 2000.
9. R. Hecht-Nielsen, "Komogorov's mapping neural network existence theorem," in Proc. IEEE Int. Conf. Neural Netw., vol. 3, San Diego, CA, 1987, pp. 11-14.
10. O. Huwendiek and W. Brockmann, "Function approximation with decomposed fuzzy systems," Fuzzy Sets Syst., vol. 101, pp. 273-296, 1999.
11. B. Igelnik and N. Parikh, "Kolmogorov's spline network," IEEE Trans. Neural Netw., vol. 14, no. 4, pp. 725-733, Jul. 2003.
12. J.-S. Jang, "ANFIS: Adaptive-network-based fuzzy inference system," IEEE Trans. Syst., Man, Cybern., vol. 23, no. 3, pp. 665-685, May/Jun. 1993.
13. M. G. Joo and J. S. Lee, "A class of hierarchical fuzzy systems with constraints on the fruzzy rules," IEEE Trans. Fuzzy Syst., vol. 13, no. 2, pp. 194-203, Apr. 2005.
14. M. Kumar, R. Stoll, and N. Stoll, "A min-max approach to fuzzy clustering, estimation, and identification," IEEE Trans. Fuzzy Syst. vol. 14, no. 2, pp. 248-262, Apr. 2006.
15. B. Kosko, "Fuzzy systems as universal approximators," in Proc. IEEE Int. Conf. Fuzzy Syst., San Diego, CA, Mar. 1992, pp. 1153-1162.
16. R. J. Kuo, S. C. Chi, and S. S. Kao, "A decision support system for selecting convenience store location through integration fuzzy AHP and artificial neural networks," Comput. Ind., vol. 47, pp. 199-214, 2002.
17. M. Landajo, M. J. Rio, and R. Perez, "A note on smooth approximation capabilities of fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 9, no. 2, pp. 229-236, Apr. 2001.
18. G. G. Lorentz, Approximation of Functions. New York: Holt, Reinhart and Winston, 1966.
19. T. Poggio and F. Girosi, "A theory of networks for approximation and learning," Artif. Intell. Lab., MIT, Cambridge, A.I. Memo No. 1140, 1989.
20. M. J. D. Powell, Approximation Theory and Methods. Cambridge, U.K.: Cambridge Univ. Press, 1981.
21. D. Rogers, "A review of sales forecasting models most commonly applied in retail site evaluation," Int. J. Retail Distrib. Manage., vol. 20, no. 4, pp. 3-11, 1992.
22. F. Scarselli and T. A. Chung, "Universal approximation using feedforward neural networks: A survey of some existing methods, and some new results," Neural Netw., vol. 11, pp. 15-37, 1998.
23. G. A. F. Seber and C. J. Wild, Nonlinear Regression. New York: Wiley, 2003.
24. A. J. Smola and B. Schölkopf, "A tutorial on support vector regression," Stat. Comput., vol. 14, pp. 199-222, 2004.
25. A. J. Smola and B. Schölkopf, "On a kernel-based method for pattern recognition, regression, approximation and operator inversion," Algorithmica, vol. 22, pp. 211-231, 1998.
26. D. A. Sprecher, "A representation theorem for continuous functions of several variables," in Proc. Amer. Math. Soc., 1965, vol. 16, pp. 200-203.
27. D. A. Sprecher, "A numerical implementation of Kolmogolov's superpositions II," Neural Netw., vol. 10, pp. 447-457, 1997.
28. V. Torra, "A review of the construction of hierarchical fuzzy systems," Int. J. Intell. Syst., vol. 17, pp. 531-543, 2002.
29. V. Vapink, S. Golowich, and A. Smola, "Support vector method for function approximation, regression estimation, and signal processing," in Advances in Neural Information Processing Systems 9, M. C. Mozer, M. I. Jordan, and T. Petsche, Eds. Cambridge, MA: MIT Press, 1997, pp. 281-287.
30. D. Wang, X.-J. Zeng, and J. A. Keane, "Hierarchical hybrid fuzzy-neural networks for approximation with mixed input variables," Neurocomputing, vol. 70, pp. 3019-3033, 2007.
31. L.-X. Wang, "Fuzzy systems are universal approximators," Proc. IEEE Int. Conf. Fuzzy Syst., San Diego, CA, Mar. 1992, Vol. SMC7, no. 10, pp. 1163-1170.
32. L.-X. Wang. A Course in Fuzzy Systems and Control. Upper Saddle River, NJ: Prentice-Hall, 1997.
33. L.-X. Wang, "Analysis and design of hierarchical fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 7, no. 5, pp. 617-624, Oct. 1999.
34. F. Witlox and H. Timmermans, "MATISSE: A knowledge-based system for industrial site selection and evaluation," Comput., Environ. Urban Syst., vol. 24, pp. 23-43, 2000.
35. Hi Ying, "Sufficient conditions on general fuzzy systems as function approximations," Automatica, vol. 30, pp. 521-525. 1994.
36. 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, 773-778, Dec. 2000.
37. X.-J. Zeng and M. G. Singh, "Approximation accuracy analysis of fuzzy systems as function approximators," IEEE Trans. Fuzzy Systems, vol. 4, no. 1, pp. 44-63, Feb. 1996.
38. X.-J. Zeng and M. G. Singh, "Decomposition property of fuzzy systems and its applications," IEEE Trans. Fuzzy Syst., vol. 4, no. 2, pp. 149-165, May 1996.
39. X.-J. Zeng and J. A. Keane, "Approximation capabilities of hierarchical fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 13, no. 5, pp. 659-672, Oct. 2005.
40. X.-J. Zeng, J. Y. Goulerma, J. A. Keane, and P. Liatsis, "Approximation capabilities of hierarchical neural-fuzzy for function approximation on discrete spaces," Int. J. Comput. Intell. Res., vol. 1, pp. 29-41, 2005.