[1] Shen Ruiling, Han Zhengzhong,. New sufficient conditions for general linear SISOTakagi-Sugeno fuzzy systems as universal approximators [J]. Journal of Southeast University (English Edition), 2005, 21 (3): 375-378. [doi:10.3969/j.issn.1003-7985.2005.03.025]

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New sufficient conditions for general linear SISOTakagi-Sugeno fuzzy systems as universal approximators()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

21

Issue:

2005 3

Page:

375-378

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2005-09-30

Info

Title:

New sufficient conditions for general linear SISOTakagi-Sugeno fuzzy systems as universal approximators

Author(s):

Shen Ruiling;  Han Zhengzhong

Department of Mathematics, Southeast University, Nanjing 210096, China

Keywords:

Takagi-Sugeno(TS)fuzzy system;  universal approximator;  sufficient condition

PACS:

O159

DOI:

10.3969/j.issn.1003-7985.2005.03.025

Abstract:

By the best approximation theory, it is first proved that the SISO(single-input single-output)linear Takagi-Sugeno(TS)fuzzy systems can approximate an arbitrary polynomial which, according to Weierstrass approximation theorem, can uniformly approximate any continuous functions on the compact domain. Then new sufficient conditions for general linear SISO TS fuzzy systems as universal approximators are obtained. Formulae are derived to calculate the number of input fuzzy sets to satisfy the given approximation accuracy. Then the presented result is compared with the existing literature’s results. The comparison shows that the presented result needs less input fuzzy sets, which can simplify the design of the fuzzy system, and examples are given to show its effectiveness.

References:

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[4] Zeng X J, Singh M G. Approximation theory of fuzzy systems—SISO case [J]. IEEE Trans on Fuzzy Syst, 1994, 2(2): 162-176.
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[6] Ying H. Sufficient conditions on general fuzzy systems as function approximators [J]. Automatica, 1994, 30(3): 521-525.
[7] Ying H. General SISO Takagi-Sugeno fuzzy systems with linear rule consequent are universal approximators [J]. IEEE Trans on Fuzzy Syst, 1998, 6(4): 582-587.
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[9] Kincaid David, Cheney Ward. Numerical analysis: mathematics of scientific computing. 3rd ed [M]. Beijing: China Machine Press, 2003.405-419.
[10] Filev D P, Yager R R. A generalized defuzzification method via BAD distributions [J]. Int J Intell Syst, 1991, 6(7): 687-697.

Memo

Memo:

Biographies: Shen Ruiling(1981—), female, graduate;Han Zhengzhong(corresponding author), male, professor, hanzz65@sohu.com.

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