基于粗糙集的神经网络函数逼近理论

Neural Network Function Approximation Based on Rough Sets

首先给出了神经网络函数在粗糙集意义下的下、上近似函数 ,从函数逼近的观点出发分析 ,得出对任一神经网络函数在粗糙集意义下 ,都可根据学习样本点维数找到两个关联的离散函数来逼近它 ,并且证明了在粗糙集意义下逼近的过程是可行的。该结论有助于理解粗糙集函数与神经网络函数之间的联系 ,为今后进一步研究在粗糙集意义下神经网络函数整体逼近理论及学习算法的描述奠定了基础。

In this paper,we first present the lower and upper approximation functions of a neural network function based on rough sets.An analysis based on function approximation shows that any neural network function can always find two associated discrete functions to approximate it under the concept of rough set,and proves that such an approximation process is feasible.The conclusion is helpful for people to understand the relationships between rough set functions and neural network functions,and lays a foundation for the description of a learning algorithm under such an approximation.