Approximation of fuzzy-valued functions by regular fuzzy neural networks and the accuracy analysis

In this paper, it is shown that four-layer regular fuzzy neural networks can serve as universal approximators for the sendograph-metric-continuous fuzzy-valued functions. The proof is constructive. We propose a principled method to design four-layer regular fuzzy neural neural network to approximate the target functions. In the previous work, a step function is used as the activation function. To improve the approximation accuracy, in the present work, we also consider using a semi-linear sigmoidal function as the activation function. Then it shows how to design the regular fuzzy neural networks (RFNNs) when the activation functions are the semi-linear sigmoidal function and the step function, respectively. After analyze the approximation accuracy of these two classes of RFNNs, it is found that the former has a much better performance than the latter in approximation accuracy. This conclusion also holds when the target functions satisfy other types of continuity. So the results in this paper can also be used to improve the related work. At last, we give a simulation example to validate the theoretical results.