两类新的基于T/S范数的模糊神经元模型及其应用

Two New Neuron Models Based on T/S Norms and Their Applications

基于T范数和S范数提出了F1型和F2型两类神经元模型 ,并研究了它们的性质和应用 (F1型灵敏性强而鲁棒性弱 ,而F2型神经元灵敏性弱而鲁棒性强 ) ;给出了一个基于F1型神经元的广义AND/OR运算为T/S范数簇的充分必要条件 ;首先提出了弱界三角范数的概念 ,并发现F2型的一个特例模型能实现弱界三角范数 .经分析 ,F1型更适合用于工业控制系统 ,而F2型更适合用于面向用语言描述知识的医学和人文社会领域的计算机应用系统 .该文把一个由特殊的F2型神经元组成的神经网络用于模糊推理 ,发现该推理方法是Zadeh的CRI法的推广 ,且能满足假言推理 .通过权值的调整 ,该推理法能满足若干推理原则的要求 .

Based on T norm/ S norm, F 1 and F2 fuzzy neuron models are proposed for the first time in the paper. Their properties and applications are discussed here. F1 model holds good sensitivity and poor robustness. However F2 model holds good robustness and poor sensitivity. The paper presents a necessary and sufficient condition of that a generalized AND/OR operator based on F1 model is a weak T norm/ S norm cluster. The paper set forth the concept of weak bound triangular norm for the first time, further, finds out a particular F2 model which can realize weak bound triangular norm. Then the paper points out that F1 model is more suitable for industrial control systems and F2 model is more suitable for those computer application systems such as fuzzy expert system in the fields of medicine, law and strategic decision et al. Finally, a fuzzy neural network based on a particular F2 neuron is applied in fuzzy inference. The new inference method generalizes traditional Zadeh’s CRI and satisfies modus ponens and other inference principles when the weights are adjusted in right way.