Sobolev approximation by means of fuzzy systems with overlapping Gaussian concepts

In this paper the approximating capabilities of fuzzy systems with overlapping Gaussian concepts are considered. A new method for the computation of the system coefficients is provided, showing that it guarantees uniform approximation of the derivatives of the target function. Moreover, the connection with radial basis functions approximations is highlighted.

[1]  Giuseppe De Nicolao,et al.  Consistent identification of NARX models via regularization networks , 1999, IEEE Trans. Autom. Control..

[2]  Jooyoung Park,et al.  Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.

[3]  Xiao-Jun Zeng,et al.  Approximation theory of fuzzy systems-SISO case , 1994, IEEE Trans. Fuzzy Syst..

[4]  Tomaso A. Poggio,et al.  Regularization Theory and Neural Networks Architectures , 1995, Neural Computation.

[5]  R. Rovatti,et al.  Takagi-Sugeno models as approximators in Sobolev norms: the SISO case , 1996, Proceedings of IEEE 5th International Fuzzy Systems.

[6]  G. Wahba.  Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy , 1977 .

[7]  M. Newman,et al.  Interpolation and approximation , 1965 .

[8]  F. Girosi,et al.  Networks for approximation and learning , 1990, Proc. IEEE.

[9]  Riccardo Rovatti,et al.  Fuzzy piecewise multilinear and piecewise linear systems as universal approximators in Sobolev norms , 1998, IEEE Trans. Fuzzy Syst..

[10]  James J. Buckley,et al.  Universal fuzzy controllers , 1992, Autom..

[11]  R. Rovatti,et al.  On the approximation capabilities of the homogeneous Takagi-Sugeno model , 1996, Proceedings of IEEE 5th International Fuzzy Systems.

[12]  Federico Girosi,et al.  An Equivalence Between Sparse Approximation and Support Vector Machines , 1998, Neural Computation.

[13]  Joos Vandewalle,et al.  Fuzzy systems as universal approximators : Constructive theory , 1997 .

[14]  N. Aronszajn.  Theory of Reproducing Kernels. , 1950 .