模糊神经网络中一个组合恒等式的新证法

A New Proof of the Combinatorial Identity in Fuzzy Neural Network

针对模糊神经网络的泛逼近性研究中遇到的一个重要组合恒等式问题,借助于二项式定理的展开式,反复通过配项、拆项、求导数等初等方法,从而巧妙地获得了证明,该组合恒等式的证明直观扼要,为进一步研究模糊神经网络的泛逼近性问题提供了一种有效途径。

An important combinatorial identity in the study of universal approximation ot fuzzy neural network was proved. According to the binomial theorem expansion of the identity, the proof was done skillfully by some elementary methods, including item - match, item - decomposition and differential. The proof of this combinatorial identity is direct and brief, thus providing an effective way for further study of universal approximation of fuzzy neural network.