A traditional neuro-fuzzy system is transformed into an equivalent fully connected three layer neural network (NN), namely, the fully connected neuro-fuzzy inference systems (F-CONFIS). The F-CONFIS differs from traditional NNs by its dependent and repeated weights between input and hidden layers and can be considered as the variation of a kind of multilayer NN. Therefore, an efficient learning algorithm for the F-CONFIS to cope these repeated weights is derived. Furthermore, a dynamic learning rate is proposed for neuro-fuzzy systems via F-CONFIS where both premise (hidden) and consequent portions are considered. Several simulation results indicate that the proposed approach achieves much better accuracy and fast convergence.