Stability Analysis Of Fuzzy Hopfield Neural Networks

In 1987, since B.Kosko defined the'max-min'neural networks as the fuzzy associative memories, the research has been attracted many scholar's attention. Fuzzy associative memories models integrate the advantages of both fuzzy systems and neural networks in dealing with information. And they have found very useful in many practical areas, for instance, knowledge engineering,pattern recognition,control and decision making and so on.The fuzzy operator composition"max-min"can characterize the essential of a lot of practical problems, and it can also be used to extend classical information (binary information) to fuzzy information. On the other hand, the composition"max-min"take only into account the primary factors and neglect the secondary factors, so a lot of information wasted, which takes disadvantage of charactering the practicality problems. Therefore, in order to enlarge the applications of the fuzzy neural networks, many scholars concentrate their attention upon how to set up the network models based on general fuzzy operators.In this paper, a general dynamical fuzzy neural network model—fuzzy Hopfield networks with threshold is developed, which is based on the fuzzy operator composition of max(∨) and weakly continuous T -norms. It is shown that the model is global stable with the Hamming distance, and its equilibrium point (attractor) is Lyapunov stable. Finally, a simulation example is employed to demonstrate our conclusions.