基于爱因斯坦t-模的模糊联想记忆的学习算法

An Efficient Learning Algorithm for Fuzzy Associative Memory Based on Einstain's t-Norm

为神经网络提供有效学习算法是神经网络研究的关键问题。文章利用t-模的伴随蕴涵算子,为基于Max和Tes合成的模糊联想记忆网络Max-TesFAM提供了一种新的学习算法,此处Tes是由爱因斯坦提出的一种t-模算子。从理论上严格证明了,只要Max-TesFAM能完整可靠地存储所给的多个模式对,则该新的学习算法一定能找到使得网络能完整可靠存储这些模式对的所有连接权矩阵的最大者。最后,用实验说明了所提出的学习算法的有效性。

The key issue for research on a neural network is to find efficient learning algorithm for the network. Taking advantage of the concomitant implication operator of To,,which is a t-norm and was presented by Einstein,a simple efficient learning algorithm is proposed for the fuzzy associative memory based on fuzzy composition of Max and Tes（Max-Tes FAM）.It is proved theoretically that,for arbitrary given training pattern pairs,if the Max-Tes, FAM has ability to store reliably them,then the proposed learning algorithm can find the maximum of all connected weight matrices which can ensure that the Max-Tes, FAM stores reliably these pattern pairs.Finally an experiment is given to illustrate the effectivity of the presented learning algorithms.