TY - JOUR
T1 - Function Approximation Using Fuzzy Neural Networks with Robust Learning Algorithm
AU - Wang, Wei Yen
AU - Lee, Tsu Tian
AU - Liu, Ching Lang
AU - Wang, Chi Hsu
N1 - Funding Information:
Manuscript received September 22, 1995; revised February 21, 1996. This work was supported by the National Science Council, R.O.C., under Grant NSC 83-0404-E-011-046. W.-Y. Wang is with the Department of Electronic Engineering, St. John’s and St. Mary’s Institute of Technology, Taipei, Taiwan, R.O.C.. T.-T. Lee and C.-L. Liu are with the Department of Electrical Engineering, National Taiwan Institute of Technology, Taipei, Taiwan, R.O.C.. C.-H. Wang is with the Department of Microelectronic Engineering, Griffith University, Nathan, Brisbane, Queensland, Australia. Publisher Item Identifier S 1083-4419(97)02933-6.
PY - 1997/8
Y1 - 1997/8
N2 - The paper describes a novel application of the B-spline membership functions (BMF's) and the fuzzy neural network to the function approximation with outliers in training data. According to the robust objective function, we use gradient descent method to derive the new learning rules of the weighting values and BMF's of the fuzzy neural network for robust function approximation. In this paper, the robust learning algorithm is derived. During the learning process, the robust objective function comes into effect and the approximated function will gradually be unaffected by the erroneous training data. As a result, the robust function approximation can rapidly converge to the desired tolerable error scope. In other words, the learning iterations will decrease greatly. We realize the function approximation not only in one dimension (curves), but also in two dimension (surfaces). Several examples are simulated in order to confirm the efficiency and feasibility of the proposed approach in this paper.
AB - The paper describes a novel application of the B-spline membership functions (BMF's) and the fuzzy neural network to the function approximation with outliers in training data. According to the robust objective function, we use gradient descent method to derive the new learning rules of the weighting values and BMF's of the fuzzy neural network for robust function approximation. In this paper, the robust learning algorithm is derived. During the learning process, the robust objective function comes into effect and the approximated function will gradually be unaffected by the erroneous training data. As a result, the robust function approximation can rapidly converge to the desired tolerable error scope. In other words, the learning iterations will decrease greatly. We realize the function approximation not only in one dimension (curves), but also in two dimension (surfaces). Several examples are simulated in order to confirm the efficiency and feasibility of the proposed approach in this paper.
KW - Function approximation
KW - fuzzy neural network
KW - robust learning algorithm
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U2 - 10.1109/3477.604123
DO - 10.1109/3477.604123
M3 - Article
AN - SCOPUS:0031212001
SN - 1083-4419
VL - 27
SP - 740
EP - 747
JO - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
JF - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IS - 4
ER -