): the weight between the u-th neuron in the m-th layer and the v-th neuron in the (m+1)-th layer, m =1 to M ??? 1;u = 1 to Nm; v =1 to Nm+1.The fuzzy neural network is applied to diagnose the fault types of a rolling bearing by the sequential diagnosis algorithm, and realized with a developed back propagation neural network called as ???the partially-linearized neural network??? (PLNN).