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中文摘要：
提出了结构简单的分式线性神经网络，证明该种神经网络可无限逼近R^m上有界闭子集到R^n上的任意连续映射，同时，证实该种神经网络可无限逼近R^m上无界闭子集到R^n上的在无穷远有极限的任意连续映射，扩充了BP神经网络的非线性逼近能力；给出了实现分式线性神经网络逼近有界或无界区域上连续映射的反向传播算法．仿真实验表明所给出的反向传播算法可行有效．该结果为无界区域上的分类问题和决策问题的解决提供了理论基础．
英文摘要：
This paper presents a fractional linear neural network with simple structure, and proves that the fractional linear neural network can limitlessly approach any continuous mapping from limited close subset of R^m to R^n. The neural network also can limitlessly approach any continuous mapping, which has limit at infinite place, from limitless close subset of R^m to R^n. It ex tends the nonlinear approach ability of traditional BP neural network. Moreover the back propa gation algorithm for a fractional linear neural network to approach any continuous mapping on limited or limitless field is proposed. The simulations show that the back propagation algorithm proposed is feasible and effective. The results offer theoretical basis for the resolution of class and decision making on limitless field.
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