训练模式对的摄动对折线模糊神经网络稳定性的影响  

Influence of Perturbations of Training Pattern Pairs on Stability of Polygonal Fuzzy Neural Network

作　　者：隋晓琳[1] 王贵君[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《模式识别与人工智能》2012年第6期928-936,共9页Pattern Recognition and Artificial Intelligence

基　　金：国家自然科学基金资助项目(No.60974144)

摘　　要：引入折线模糊数及其扩张运算,针对折线模糊神经网络,定义折线模糊数的最大摄动误差、训练模式对的γ摄动等概念,并基于纠错规则设计该网络连接权的学习算法.其次,当转移函数满足Lipschitz条件和训练模式对发生γ摄动时,在定义折线模糊神经网络对训练模式对摄动的全局稳定性的基础上,应用归纳法证明三层折线模糊神经网络的连接权具有稳定性,进而获得该网络关于训练模式对的γ摄动也具有全局稳定性.最后,通过模拟实例说明训练模式对的摄动对该网络稳定性的影响.The concepts of the maximum perturbation error of polygonal fuzzy numbers and T-perturbation of training pattern pairs are put forward, and the learning algorithm of connection weight is designed according to error-correction rules by introducing polygonal fuzzy numbers and their operations. Then the definition of the global stability of the polygonal fuzzy neural networks of the perturbation of training pattern pairs is introdued. Secondly, whenever the transfer function satisfies the Lipschitz condition and y-perturbation occurs in the training pattern pairs, the stability of the connections of the three-layer polygonal fuzzy neural networks is proved by applying mathematical induction. Moreover, that the T-perturbation of this network with respect to the training pattern pairs possesses the global stability is obtained. Finally, the influence of perturbations of training pattern pairs on the stability of polygonal fuzzy neural networks is explained by the simulative examples.

关 键 词：折线模糊数 折线模糊神经网络 训练模式对 全局稳定性 摄动 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程] O159[自动化与计算机技术—控制科学与工程]