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CLC number: TP13
On-line Access: 2016-06-06
Received: 2016-02-23
Revision Accepted: 2016-04-28
Crosschecked: 2016-05-23
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Derivation and analysis on the analytical structure of interval type-2 fuzzy controller with two nonlinear fuzzy sets for each input variable
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Bin-bin Lei, Xue-chao Duan, Hong Bao, Qian Xu. Derivation and analysis on the analytical structure of interval type-2 fuzzy controller with two nonlinear fuzzy sets for each input variable[J]. Frontiers of Information Technology & Electronic Engineering, 2016, 17(6): 587-602.
@article{title="Derivation and analysis on the analytical structure of interval type-2 fuzzy controller with two nonlinear fuzzy sets for each input variable",
author="Bin-bin Lei, Xue-chao Duan, Hong Bao, Qian Xu",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="17",
number="6",
pages="587-602",
year="2016",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1601019"
}
%0 Journal Article
%T Derivation and analysis on the analytical structure of interval type-2 fuzzy controller with two nonlinear fuzzy sets for each input variable
%A Bin-bin Lei
%A Xue-chao Duan
%A Hong Bao
%A Qian Xu
%J Frontiers of Information Technology & Electronic Engineering
%V 17
%N 6
%P 587-602
%@ 2095-9184
%D 2016
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1601019
TY - JOUR
T1 - Derivation and analysis on the analytical structure of interval type-2 fuzzy controller with two nonlinear fuzzy sets for each input variable
A1 - Bin-bin Lei
A1 - Xue-chao Duan
A1 - Hong Bao
A1 - Qian Xu
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 17
IS - 6
SP - 587
EP - 602
%@ 2095-9184
Y1 - 2016
PB - Zhejiang University Press & Springer
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DOI - 10.1631/FITEE.1601019
Abstract: Type-2 fuzzy controllers have been mostly viewed as black-box function generators. Revealing the analytical structure of any type-2 fuzzy controller is important as it will deepen our understanding of how and why a type-2 fuzzy controller functions and lay a foundation for more rigorous system analysis and design. In this study, we derive and analyze the analytical structure of an interval type-2 fuzzy controller that uses the following identical elements: two nonlinear interval type-2 input fuzzy sets for each variable, four interval type-2 singleton output fuzzy sets, a Zadeh AND operator, and the karnik-Mendel type reducer. Through dividing the input space of the interval type-2 fuzzy controller into 15 partitions, the input-output relationship for each local region is derived. Our derivation shows explicitly that the controller is approximately equivalent to a nonlinear proportional integral or proportional differential controller with variable gains. Furthermore, by comparing with the analytical structure of its type-1 counterpart, potential advantages of the interval type-2 fuzzy controller are analyzed. Finally, the reliability of the analysis results and the effectiveness of the interval type-2 fuzzy controller are verified by a simulation and an experiment.
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