A Learning Algorithm Of Fuzzy Associative Memory Based On The Fault-Tolerance

Fuzzy neural network with its learning algorithm is a research concentration in artificial intelligence domain at present. Around the learning algorithm of Fuzzy Associative Memory (FAM) network, the robustness and fault-tolerance performance of∨-T FAM is studied in the paper, with which V is fuzzy max operation and T is T-Norms. The main works can be listed as follows:(1)This paper sets up a class of fuzzy associative memories based on the fuzzy compos-ition of fuzzy max operation (∨) and T-Norms, so called∨-T FAM. With the fuzzy implic-ation operator of T-Norms, a general learning algorithm is proposed for a class of such∨-T FAMs. Since small perturbations of training pattern pairs may caused some disadvantage to performance of a fuzzy neural network, so a new concept is established for the robustness of∨-T FAMs to perturbations of training pattern pairs. The theoretical studies show that when T-Norms satisfy Lipschitz condition,∨-T FAMs have good robustness under the condition of the perturbation factor ofβ(β≥1) of training pattern pairs by this learning algorithm. Finally, the experiment with which the∨-T FAM associates an image with another image is given to testify the theoretical results.(2)Penetrating into the algorithm of above-mentioned∨-T FAM, a learning algorithm of∨-T FAM based on the fault-tolerance is designed. Firstly, we discuss the stability of the model and prove the Lyapunov stability of the equilibrium points. In addition, we show some sufficient conditions under which the fuzzy pattern is the attractor of the model and obtain a nontrivially attractive basin of the attractor. Lastly, we design an efficient learning algorithm about the connected weights of the network based on it. With some conditions, we prove all the given fuzzy patterns are the attractors of the network and the attractive basin of the attractor is nontrivially respectively. Therefore, out models have good fault-tolerance performance.