Function approximation using fuzzy neural networks with robust learning algorithm

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.