关键词: 模糊Hopfield网络，平衡点，学习算法，稳定性，鲁棒性

Abstract: In this paper, an efficient learning algorithm was proposed for a class of fuzzy Hopfield networks(Max-T FHNNs) based on I=norms. For any given set of patterns, the learning algorithm can find the maximum of all conneclion weight matrices that can make the set become a set of the equilibrium points of the Max-T FHNN when T is a left continuous T-norm. This maximal matrix is idempotent matrix in sense of Max-T composition, with which the Max-T FHNN can be convergent to a stable state in one iterative process for any input vector. It is proved theoretically that arbitrary set of patterns can become a set of the ectuilibrium points of every Max-T FHNN if only the T is left continuous T-norm. Max-TL FHNN has universally good robustness to perturbation of training pattern.

Key words: Hopfield network, Equilibrium point, Learning algorithm, Stability, Robustness