Abstract: The paper analyses the robustness of learning algorithm for fuzzy associative memory based on Einstain’s t-norm by using the properties of fuzzy bidirectional associative memories based on triangular norms and the overall situation robustness of fuzzy bidirectional associative memories. The conclusion that the learning algorithm can keep good overall robustness when the perturbations are positive is proved in theory and verified by experiment in this paper. And that the learning algorithm doesn’t satisfy overall situation robustness when the noise contains negative value is proved by experiment. What is more, the relation between the maximum of perturbations of training patterns and the maximum of perturbations of the output is also analyzed and the relation curve is gotten.

Key words: Einstain t-norm, fuzzy bidirectional associative memory, learning algorithm, overall situation robustness

摘要： 利用三角模的模糊联想记忆网络的性质以及模糊联想记忆网络的鲁棒性定义，对基于爱因斯坦t-模构建的模糊双向联想记忆网络的学习算法的全局鲁棒性进行了分析。从理论上证明了当训练模式的摄动为正向摄动时，该学习算法可以保持良好的鲁棒性，并用实验验证了该结论；而当摄动存在负向波动时该学习算法不满足全局鲁棒性。然后又进一步对训练模式集摄动最大摄动与输出模式集的最大摄动之间的关系进行研究，得出了训练模式集的最大摄动与输出模式集的最大摄动之间的关系曲线。

关键词: 爱因斯坦t-模, 糊联想记忆网络, 学习算法, 全局鲁棒性