Aimed at the characteristics of strong nonlinearity, uncertainty, time-variance and serious interconnection etc for AC electric arc-furnace (EAF). A new control method is put forward, in which fuzzy-neural network is applied. Mamdani fuzzy model is adopted in the control system, its structure has four layers. According to the gradient descent strategy, the variable learning speed algorithm of the off-line is used to seek for the better parameters of membership function and the weights of the links between layer III and layer W, the invariable learning speed algorithm of the on-line is used to ...