The development of neuro-fuzzy systems by integrating neural networks and fuzzy systems is desired because such systems can adjust fuzzy membership functions and produce fuzzy inference rules by case-learning without the need for experts or experiments. It has been applied to various fields, but there has been no detailed study of the various neuro-fuzzy models applicable to rule generation. In this paper, an experimentally verified five-layer and three-phase network is presented, which shows the effectiveness with which the neuro-fuzzy system automatically determines membership functions and selects activation fuzzy rules using both system identification and vibration control examples in engineering applications.