TY - GEN
T1 - Optimal necessary conditions for general SISO Mamdani fuzzy systems as function approximators within a given accuracy
AU - Sun, Fuchun
AU - Yang, Jin
AU - Luo, Minnan
AU - Liu, Huaping
PY - 2011
Y1 - 2011
N2 - In this paper, necessary conditions are investigated for a single input/single output (SISO) Mamdani fuzzy systems as function approximators of continuous functions within a given accuracy. Since general SISO Mamdani fuzzy systems are monotonic on subintervals, the optimal configuration of fuzzy systems is that the number of division points is at least the times of its monotonicity changes. Thus with the extreme of the desired continuous function, necessary conditions are obtained through generating intervals that contain division points and pruning redundant intervals. Furthermore, a dynamically constructive method is proposed to show the conditions are optimal. It has been shown that existing results concerning necessary conditions are only special cases of our results. Finally, simulation examples are given to illustrate the conclusions, the strength of the fuzzy systems as function approximators are analyzed.
AB - In this paper, necessary conditions are investigated for a single input/single output (SISO) Mamdani fuzzy systems as function approximators of continuous functions within a given accuracy. Since general SISO Mamdani fuzzy systems are monotonic on subintervals, the optimal configuration of fuzzy systems is that the number of division points is at least the times of its monotonicity changes. Thus with the extreme of the desired continuous function, necessary conditions are obtained through generating intervals that contain division points and pruning redundant intervals. Furthermore, a dynamically constructive method is proposed to show the conditions are optimal. It has been shown that existing results concerning necessary conditions are only special cases of our results. Finally, simulation examples are given to illustrate the conclusions, the strength of the fuzzy systems as function approximators are analyzed.
KW - approximation accuracy
KW - fuzzy rules
KW - fuzzy systems
KW - necessary conditions
UR - https://www.scopus.com/pages/publications/80053088250
U2 - 10.1109/FUZZY.2011.6007674
DO - 10.1109/FUZZY.2011.6007674
M3 - 会议稿件
AN - SCOPUS:80053088250
SN - 9781424473175
T3 - IEEE International Conference on Fuzzy Systems
SP - 2319
EP - 2326
BT - FUZZ 2011 - 2011 IEEE International Conference on Fuzzy Systems - Proceedings
T2 - 2011 IEEE International Conference on Fuzzy Systems, FUZZ 2011
Y2 - 27 June 2011 through 30 June 2011
ER -