模糊联想记忆对训练模式对摄动的鲁棒性研究

Robustness research of fuzzy associative memories with perturbation of training pattern pairs

基于模糊取大算子(V)和T-模的模糊合成,构建了一类模糊联想记忆网络(V-T FAM)。利用T-模的模糊蕴涵算子,给出了这类V-T FAM的学习算法。针对训练模式对小幅摄动可能对模糊神经网络的性能产生副作用,提出V-T FAM对训练模式对摄动的鲁棒性概念。理论研究表明,当T-模满足Lipschitz条件时,采用上述学习算法的V-TFAM对训练模式对摄动幅度,在系数为β的条件下全局拥有好的鲁棒性。最后用V-T FAM在图像联想方面的实验验证了理论结果。

This paper sets up a class of fuzzy associative memories based on the fuzzy composition of max operation（V） and T-Norms,so be called V-T FAM（Fuzzy Associative Memory）.With the fuzzy implication operator of T-Norms,a general learning algorithm is proposed for a class of such V-T FAMs.Since small perturbations of training pattern pairs may cause some disadvantages to performance of a fuzzy neural network,a new concept is established for the robustness of V-T FAMs to perturbations of training pattern pairs.The theoretical researches show that when T-Norms satisfy Lipschitz condition,V-T FAMs have good robustness under the condition of the perturbation factor of β of training pattern pairs by the proposed learning algorithm.Finally,the experiment with which the V-T FAM associated an image with another image is given to testify the theoretical results.