Are fuzzy systems universal approximators?

International Journal of General Systems

Volumn 28, Issue 2, 1999, Pages 259-282

  Klement, Erich Peter ^a   Kóczy, László T ^a,b,c   Moser, Bernhard ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^b BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^c Tokyo Institute of Technology ^*  (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL LINGUISTICS; THEOREM PROVING;

UNIVERSAL APPROXIMATORS;

FUZZY SETS;

EID: 0342298575     PISSN: 03081079     EISSN: None     Source Type: Journal    
DOI: 10.1080/03081079908935238     Document Type: Article

References (44)

1. Bauer, P., Klement, E.P., Moser, B. and Leikermoser, A. (1993) "Approximation of real functions by rule bases." Proceedings of the International Fuzzy Systems Association Congress, Seoul, pp. 239-241.
2. Bauer, P., Klement, E.P., Moser, B. and Leikermoser, A. (1994) "Interpolation and approximation of real input output functions using fuzzy rule bases." In: Fuzzy Systems in Computer Science, edited by R. Kruse, J. Gebhardt and R. Palm, Vieweg, Braunschweig, pp. 245-254.
3. Bauer, P., Klement, E.P., Moser, B. and Leikermoser, A. (1995) "Modeling of control functions by fuzzy controllers." In: Theoretical Aspects Fuzzy Control, edited by H. Nguyen, M. Sugeno, R. Tong and R.R. Yager, John Wiley, New York, pp. 91-116.
4. Buckley, J.J. (1993a) "Controllable processes and the fuzzy controller." Fuzzy Sets and Systems, 53, pp. 27-31.
5. Buckley, J.J. (1993b) "Sugeno type controllers are universal controllers." Fuzzy Sets and Systems, 53, pp. 299-304.
6. Buckley, J.J. (1995) "Systems stability and the fuzzy controller." In: Theoretical Aspects of Fuzzy Control, edited by H. Nguyen, M. Sugeno, R. Tong and R.R. Yager, John Wiley, New York, pp. 51-63.
7. Burkhardt, D.G. and Bonissone, P. (1993) "Automated fuzzy knowledge base generation and tuning." Proceedings of the first IEEE International Conference on Fuzzv Systems, San Diego, pp. 179-196.
8. Castro, J. (1995) "Fuzzy logic controllers are universal approximators." IEEE Transactions on Systems, Man and Cybernetics, 25, 629-635.
9. Driankov, D., Hellendoorn, H. and Reinfrank, M. (1993) "An introduction to fuzzy control." (Springer, New York, Berlin).
10. Dubois, D. and Prade, H. (1988) "Possibility theory: an approach to computerized processing of uncertainty." (Plenum Press, New York).
11. Dubois, D., Grabisch, M. and Prade, H. (1992) "Gradual rules and the approximation of functions." Proceedings of the International Fuzzy Systems Association Congress. Iizuka, pp. 629-632.
12. El Hajjaji, A. and Rachid, A. (1994) "Explicit formulas for fuzzy controllers." Fuzzy Sets and Systems, 62, 135-141.
13. Foo, N. (1994) "New Perspectives and old Problems . . . " (To appear)
14. Gottwald, S. (1994) "Fuzzy sets and fuzzy logic. Foundation of applications - from a mathematical point of view." (Vieweg, Wiesbaden).
15. Hilbert, D. (1900) "Mathematische Probleme." Nachrichten der Akademie der Wissenschaften, Göttingen, pp. 290-329.
16. Kacprzyk, J. (1993) "Interpolative reasoning in optimal fuzzy control.", Proceedings of the second IEEE International Conference on Fuzzy Systems, San Francisco, pp. 1259-1263.
17. Kahane, J.P. (1975) "Sur le theorème de superposition de kolmogorov." Journal of Approximation Theory, 13, 229-234.
18. Kóczy, L.T. and Hirota, K. (1993) "Interpolative reasoning with insufficient evidence in sparse fuzzy rule bases." Information Sciences, 71, 169-201.
19. Kóczy, L.T. and Hirota, K. (1993b) "Approximate reasoning by linear rule interpolation and general approximation." Journal of Approximate Reasoning, 9, 197-225.
20. Kóczy, L.T., Maeda, Y., Ramerand, A. and Hiller, F. (1994) "Defuzzification in fuzzy control by normalized maximum possibility." Technical Report 93-94/407, LIFE Chair of Fuzzy Theory, Tokyo Institute of Technology, Yokohama.
21. Kóczy, L.T. and Sugeno, M. (1994) "Explicit formulas for fuzzy control and the approximator property." Technical Report 93-94/408, LIFE Chair of Fuzzy Theory, Tokyo Institute of Technology, Nagatsuta, Yokohama.
22. Kolmogorov, A.N. (1997) "On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition." Doklady Akademii Nauk SSSR, 114, 953-956.
23. Kosko, B. (1992) "Fuzzy systems as universal approximates." Proceedings of the first IEEE International Conference on Fuzzy Systems, San Diego, pp. 1153-1162.
24. Kruse, R. and Meyer, K.D. (1987) "Statistics with vague data." (Reidel, Dordrecht).
25. Kwong, C.P. (1993) "Fuzzy inference without membership functions." Manuscript, Division of Information Engineering, The Chinese University of Hong Kong.
26. Lee, C.C. (1990) "Fuzzy logic in control systems, part II." IEEE Transactions on Systems, Man and Cybernetics, 20, 419-435.
27. Lee, J. and Chae, S. (1993) "Analysis on function duplicating capabilities of fuzzy controllers." Fuzzy Sets and Systems, 56, 127-143.
28. Lorentz, G.G. (1962) "Metric entropy, widths and superposition of functions." American Mathematical Monthly, 65, 469-485.
29. Mamdani, E.H. and Assilian, S. (1975) "An experiment in synthesis with a fuzzy logic controller." Journal of Man-Machine Studies, 7, 1-13.
30. Moser, B. (1995) "On limitations of approximating multi-dimensional functions by sugeno controllers." Proceedings of the International Fuzzy Systems Association Congress, Sao Paulo, pp. 687-679.
31. Moser, B. (1990) (in press), "Sugeno controllers with a bounded number of rules are nowhere dense." In: Fuzzy Sets and Systems.
32. Moser, B. (1996) "A new approach for representing control surfaces by fuzzy rule bases." Ph.D. Thesis, Linz, Austria, pp. 19-32.
33. Nguyen, H.T. and Kreinovich, V. (1992) "On approximations of controls by fuzzy systems." Technical Report 92-93/302, LIFE Chair of Fuzzy Theory, Tokyo Institute of Technology, Nagatsuta, Yokohama.
34. Sprecher, D.A. (1965) "On the structure of continuous functions of several variables." Transactions of the American Mathematical Society, 115, 340-355.
35. Su, C.Y. and Stepanenko, Y. (1994) "Adaptive control of a class of nonlinear systems with fuzzy logic." IEEE Transactions on Fuzzy Systems, 1(2), 285-294.
36. Sugeno, M. and Yasukawa, T. (1993) "A fuzzy-logic-based approach to qualitative modeling." IEEE Transaction on Fuzzy Systems, 1(1), 7-31.
37. Takagi, T. and Sugeno, M. (1985) "Fuzzy identification of systems and its applications to modelling and control." IEEE Transactions on Systems Man and Cybernetics, 15, 116-132.
38. Vitushkin, A.G. (1954) "On Hilbert's thirteenth problem". Doklady Akadadenii Nauk SSSR, pp. 701-704.
39. Vitushkin, A.G. and Henkin, G.M. (1967) "Linear superposition of functions." Russian Mathematical Surveys, 22, 77-125.
40. Wang, L.X. (1992) "Fuzzy systems are universal approximators." Proceedings of the IEEE International Conference on Fuzzy Systems, San Diego, pp. 1163-1169.
41. Wang, L.X. and Mendel, J.M. (1992) "Fuzzy basis functions, universal approximations and orthogonal least-squares learning." IEEE Transactions on Neural Nets, 3, 807-814.
42. Zadeh, L.A. (1995) "Fuzzy sets." Information and Control, 8, 338-353.
43. Zadeh, L.A. (1973) "Outline of a new approach to the analysis of complex systems and decision processes." IEEE Transactions on Systems, Man and Cybernetics, 3, 28-44.
44. Zadeh, L.A. (1975) "The concept of a linguistic variable and its application to approximate reasoning." Information Sciences, 1(8), 199-250.