Approximation accuracy analysis of fuzzy systems as function approximators

Author

Zeng, Xiao-Jun ; Singh, Madan G.

Author_Institution

Dept. of Comput., Univ. of Manchester Inst. of Sci. & Technol., UK

Volume

4

Issue

1

fYear

1996

fDate

2/1/1996 12:00:00 AM

Firstpage

44

Lastpage

63

Abstract

This paper establishes the approximation error bounds for various classes of fuzzy systems (i.e., fuzzy systems generated by different inferential and defuzzification methods). Based on these bounds, the approximation accuracy of various classes of fuzzy systems is analyzed and compared. It is seen that the class of fuzzy systems generated by the product inference and the center-average defuzzifier has better approximation accuracy and properties than the class of fuzzy systems generated by the min inference and the center-average defuzzifier, and the class of fuzzy systems defuzzified by the MoM defuzzifier. In addition, it is proved that fuzzy systems can represent any linear and multilinear function and explicit expressions of fuzzy systems generated by the MoM defuzzified method are given

Keywords

approximation theory; function approximation; fuzzy logic; fuzzy systems; inference mechanisms; MoM defuzzifier; approximation accuracy analysis; approximation error bounds; center-average defuzzifier; defuzzification methods; function approximators; fuzzy systems; min inference; product inference; Approximation error; Approximation methods; Fuzzy systems; Mechanical factors; Message-oriented middleware;

fLanguage

English

Journal_Title

Fuzzy Systems, IEEE Transactions on

Publisher

ieee

ISSN

1063-6706

Type

jour

DOI

10.1109/91.481844

Filename

481844