TSK Fuzzy Function Approximators: Design and Accuracy Analysis

Fuzzy systems are excellent approximators of known functions or for the dynamic response of a physical system. We propose a new approach to approximate any known function by a Takagi-Sugeno-Kang fuzzy system with a guaranteed upper bound on the approximation error. The new approach is also used to a...

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Bibliographic Details
Published in:IEEE transactions on systems, man and cybernetics. Part B, Cybernetics man and cybernetics. Part B, Cybernetics, 2012-06, Vol.42 (3), p.702-712
Main Authors: Sonbol, A. H., Fadali, M. S., Jafarzadeh, S.
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Approximation error
Approximation error bound
Computer Simulation
Decision Support Techniques
Function approximation
Fuzzy Logic
Fuzzy sets
Fuzzy systems
fuzzy Takagi-Sugeno-Kang (TSK) systems
modeling
Models, Theoretical
Pattern Recognition, Automated - methods
Polynomials
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Summary:Fuzzy systems are excellent approximators of known functions or for the dynamic response of a physical system. We propose a new approach to approximate any known function by a Takagi-Sugeno-Kang fuzzy system with a guaranteed upper bound on the approximation error. The new approach is also used to approximately represent the behavior of a dynamic system from its input-output pairs using experimental data with known error bounds. We provide sufficient conditions for this class of fuzzy systems to be universal approximators with specified error bounds. The new conditions require a smaller number of membership functions than all previously published conditions. We illustrate the new results and compare them to published error bounds through numerical examples.
ISSN:1083-4419
1941-0492
DOI:10.1109/TSMCB.2011.2174151