Approximation theory of fuzzy systems-SISO case

Author

Zeng, Xiao-Jun ; Singh, Madan G.

Author_Institution

Decision Technol. Group, Univ. of Manchester Inst. of Sci. & Technol., UK

Volume

2

Issue

2

fYear

1994

fDate

5/1/1994 12:00:00 AM

Firstpage

162

Lastpage

176

Abstract

In this paper, the approximation problem of SISO fuzzy systems is discussed. Based on the fact that fuzzy systems can be represented by a linear combination of fuzzy basic functions (FBF´s), we first give a systematic and detailed analysis of FBF´s and present five properties of FBF´s: structure similarity and compatibility between the membership functions and FBF´s, complementarity and less fuzziness of FBF´s, and composition of fuzzy systems. These properties provide a clear picture of the shape and features of FBF´s. Based on these properties of FBF´s, we obtain some basic approximation properties of fuzzy systems: basic approximation property, uniform approximation property, uniform convergent property and universal approximation property. These results reveal the basic approximation mechanism of fuzzy systems and verify a few basic ideas in the design of fuzzy systems

Keywords

approximation theory; fuzzy set theory; SISO fuzzy systems approximation; basic approximation property; complementarity; fuzzy basic functions; fuzzy systems composition; membership function compatibility; structure similarity; uniform approximation property; uniform convergent property; universal approximation property; Approximation methods; Computer aided software engineering; Control systems; Convergence; Fuzzy set theory; Fuzzy systems; Mechanical factors; Neural networks; Shape;

fLanguage

English

Journal_Title

Fuzzy Systems, IEEE Transactions on

Publisher

ieee

ISSN

1063-6706

Type

jour

DOI

10.1109/91.277964

Filename

277964