Abstract:
A piecewise multilinear and a piecewise linear model for fuzzy systems are introduced and their approximation capabilities investigated. Classical results on the approxim...Show MoreMetadata
Abstract:
A piecewise multilinear and a piecewise linear model for fuzzy systems are introduced and their approximation capabilities investigated. Classical results on the approximation of regular functions are improved showing that fuzzy systems may keep their semantic structure while approximating to any degree of accuracy not only sufficiently regular functions, but also their derivatives.
Published in: IEEE Transactions on Fuzzy Systems ( Volume: 6, Issue: 2, May 1998)
DOI: 10.1109/91.669022
References is not available for this document.
Select All
1.
S. Weber, "A general concept of fuzzy connectives negations and implications based on t-norms and t-conorms", Int. J. Fuzzy Sets Syst., vol. 11, pp. 115-134, 1983.
2.
L. A. Zadeh, "Outline of a new approach to the analysis of complex systems and decision processes", IEEE Trans. Systems Man Cybern., vol. SMC-3, pp. 28-44, Jan. 1973.
3.
W. Pedrycz, Fuzzy Control and Fuzzy Systems, 1993.
4.
L.-X. Wang and J. M. Mendel, "Fuzzy Basis functions universal approximation and orthogonal least-squares learning", IEEE Trans. Neural Networks, vol. 3, pp. 807-814, Sept. 1992.
5.
J. J. Buckley, "Universal fuzzy controllers", Automatica, vol. 28, pp. 1245-1248, 1992.
6.
B. Kosko, "Fuzzy systems as universal approximators", IEEE Trans. Comput., vol. 43, pp. 1329-1333, Nov. 1994.
7.
H. Ying, "Sufficient conditions on general fuzzy systems as function approximators", Automatica, vol. 30, pp. 521-525, 1994.
8.
T. M. Kwon and M. E. Zervakis, "A self-organizing KNN fuzzy controller and its neural network structure", Int. J. Adaptive Contr. Signal Processing, vol. 8, pp. 407-431, 1994.
9.
X.-J. Zeng and M. G. Singh, "Approximation theory of fuzzy systemsSISO case", IEEE Trans. Fuzzy Syst., vol. 2, pp. 162-176, May 1994.
10.
X.-J. Zeng and M. G. Singh, "Approximation theory of fuzzy systemsMISO case", IEEE Trans. Fuzzy Syst., vol. 3, pp. 219-235, May 1995.
11.
X.-J. Zeng and M. G. Singh, "Approximation accuracy analysis of fuzzy systems as function approximators", IEEE Trans. Fuzzy Syst., vol. 4, pp. 44-63, Feb. 1996.
12.
J.-S. R. Jang and C.-T. Sun, "Functional equivalence between radial basis function networks and fuzzy inference systems", IEEE Trans. Neural Networks, vol. 4, pp. 156-159, Jan. 1993.
13.
J. Park and I. W. Sandberg, "Universal approximation using radial-basis-function networks", Neural Computat., vol. 3, pp. 246-257, 1991.
14.
T. Chen and H. Chen, "Approximation capability to functions of several variables nonlinear functionals and operators by radial basis function neural networks", IEEE Trans. Neural Networks, vol. 6, pp. 904-910, July 1995.
15.
W. Siler and H. Ying, "Fuzzy control theory: The linear case", Int. J. Fuzzy Sets Syst., vol. 33, pp. 275-290, 1989.
16.
A. Voisin, L. Rondeau, R. Ruelas, G. Dubois and M. Lamotte, "Conditions to establish an equivalence between a fuzzy relational model and a linear model", 3rd Eur. Conf. Intell. Tech. Soft Comput., pp. 526-528, Aug. 1995.
17.
X.-J. Zeng and M. G. Singh, "Decomposition property of fuzzy systems and its applications", IEEE Trans. Fuzzy Syst., vol. 4, pp. 149-165, May 1996.
18.
T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control", IEEE Trans. Syst. Man Cybern., vol. SMC-15, pp. 116-132, Jan./Feb. 1985.
19.
R. Rovatti, "TakagiSugeno model as approximators in Sobolev norms: The SISO case", 5th IEEE Int. Conf. Fuzzy Syst., pp. 1060-1065, Sept. 1996.
20.
C. Fantuzzi and R. Rovatti, "On the approximation capabilities of homogeneous Takagi-Sugeno models", 5th IEEE Int. Conf. Fuzzy Syst., pp. 1067-1072, Sept. 1996.
21.
C. H. Choi and J. Y. Choi, "Constructive neural networks with piecewise interpolation capabilities for function approximation", IEEE Trans. Neural Networks, vol. 5, pp. 936-944, Nov. 1994.
22.
J. N. Lin and R. Unbehauen, "Canonical piecewise-linear networks", IEEE Trans. Neural Networks, vol. 6, pp. 43-50, Jan. 1995.
23.
K. Hornik, M. Stinchcombe and H. White, "Universal approximation of an unknown functions and its derivatives using multilayer feedforward networks", Neural Networks, vol. 3, pp. 551-560, 1990.
24.
H. Drucker and Y. Le Cun, "Improving generalization performance using double backpropagation", IEEE Trans. Neural Networks, vol. 3, pp. 991-997, Nov. 1992.
25.
K. Hornik, M. Stinchcombe, H. White and P. Auer, "Degree of approximation results for feedforward networks approximating unknown mappings and their derivatives", Neural Computat., vol. 6, pp. 1262-1275, Nov. 1996.
26.
G. J. Klir and T. A. Folger, Fuzzy Sets Uncertainty and Information, 1988.
27.
R. Rovatti, R. Guerrieri and G. Baccarani, "An enhanced two-level boolean synthesis methodology for fuzzy rules minimization", IEEE Trans. Fuzzy Syst., vol. 3, pp. 288-299, Aug. 1995.
28.
"Logic-based optimization of rule-based models", Fuzzy Modeling: Paradigms and Practice, pp. 264-286, 1995.
29.
T. A. Johansen, "Robust identification of Takagi-Sugeno-Kang fuzzy models using regularization", 5th IEEE Int. Conf. Fuzzy Syst., pp. 180-186, Sept. 1996.
30.
T. Poggio and F. Girosi, "Networks for approximation and learning", Proc. IEEE, vol. 78, pp. 1481-1497, Sept. 1990.
