Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1128.93035
Luo, Qiang; Yang, Wenqiang; Yi, Dongyun
Kernel shapes of fuzzy sets in fuzzy systems for function approximation.
(English)
[J] Inf. Sci. 178, No. 3, 836-857 (2008). ISSN 0020-0255

Summary: The shapes of if-part fuzzy sets affect the approximating capability of fuzzy systems. In this paper, the fuzzy systems with the kernel-shaped if-part fuzzy sets are built directly from the training data. It is proved that these fuzzy systems are universal approximators and their uniform approximation rates can be estimated in the single-input-single-output (SISO) case. On the basis of these rates, the relationships between the approximating capability and the shapes of if-part fuzzy sets are developed for the fuzzy systems. Furthermore, the {\it sinc} functions that serve as input membership functions are proved to have the almost best approximation property in a particular class of membership functions. The theoretical results are confirmed from the simulation data. In addition, the estimations of the uniform approximation rates are extended to the multi-input-single-output (MISO) case.
MSC 2000:
*93C42 Fuzzy control
03E72 Fuzzy sets (logic)

Keywords: fuzzy systems; function approximation; universal approximation; uniform approximation rates; almost best approximation

Highlights
Master Server