Approximation theory of fuzzy systems-MIMO case

Author

Zeng, Xiao-Jun ; Singh, Madan G.

Author_Institution

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

Volume

3

Issue

2

fYear

1995

fDate

5/1/1995 12:00:00 AM

Firstpage

219

Lastpage

235

Abstract

In this paper, the approximation properties of MIMO fuzzy systems generated by the product inference are discussed. We first give an analysis of fuzzy basic functions (FBF´s) and present several properties of FBF´s. Based on these properties of FBF´s, we obtain several basic approximation properties of fuzzy systems: 1) basic approximation property which reveals the basic approximation mechanism of fuzzy systems; 2) uniform approximation bounds which give the uniform approximation bounds between the desired (control or decision) functions and fuzzy systems; 3) uniform convergent property which shows that fuzzy systems with defined approximation accuracy can always be obtained by dividing the input space into finer fuzzy regions; and 4) universal approximation property which shows that fuzzy systems are universal approximators and extends some previous results on this aspect. The similarity between fuzzy systems and mathematical approximation is discussed and an idea to improve approximation accuracy is suggested based on uniform approximation bounds

Keywords

MIMO systems; approximation theory; convergence of numerical methods; function approximation; fuzzy logic; fuzzy systems; MIMO fuzzy systems; approximation theory; fuzzy basic functions; product inference; uniform approximation bounds; uniform convergence; universal approximation; Approximation methods; Computer aided software engineering; Control systems; Fuzzy control; Fuzzy systems; MIMO; Mechanical factors; Shape;

fLanguage

English

Journal_Title

Fuzzy Systems, IEEE Transactions on

Publisher

ieee

ISSN

1063-6706

Type

jour

DOI

10.1109/91.388175

Filename

388175