计算机工程与应用 ›› 2014, Vol. 50 ›› Issue (23): 73-76.

• 理论研究、研发设计 • 上一篇    下一篇

模糊Hopfield网络的收敛性与鲁棒性分析

刘  亮,徐蔚鸿   

  1. 长沙理工大学 计算机与通信工程学院,长沙 410114
  • 出版日期:2014-12-01 发布日期:2014-12-12

Convergence and robustness analysis of fuzzy Hopfield neural network

LIU Liang, XU Weihong   

  1. College of Computer & Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China
  • Online:2014-12-01 Published:2014-12-12

摘要: 收敛性与鲁棒性是模糊神经网络的两个重要性质。对带阈值的Max-T模糊Hopfield神经网络(记为Max-T-C FHNN)的收敛性及在训练模式小幅摄动情况下的鲁棒性进行了分析,从理论上给出了严格的证明。发现了采用最大权值矩阵学习算法时,Max-T-C FHNN具有良好的收敛性,同时当T模及其蕴含算子满足Lipschitz条件时,Max-T-C FHNN对训练模式摄动全局拥有好的鲁棒性,用自联想实验验证了理论的有效性。

关键词: 阈值, 模糊神经网络, Max-T模糊Hopfield神经网络, 收敛性, 鲁棒性

Abstract: Convergence and robustness are two important properties of fuzyy neural network. This paper analyses the convergence and robustness of Max-T fuzzy Hopfield neural network with threshold(called Max-T-C FHNN) in the condition of perturbations of  training patterns, which is proved theoretically. It is discovered that Max-T-C FHNN using maximum weight matrix is of excellent convergence. Max-T-C FHNN holds good robustness globally to perturbations of training patterns in the case that T-norms and its implication operator satisfy the Lipschitz condition. The self-association experiment is given to testify the theoretical results.

Key words: threshold, fuzzy neural network, Max-T fuzzy Hopfield neural network, convergence, robustness