Fuzzy system has been known to provide a framework for handling uncertainties and imprecision in real-world applications by taking linguistic information from human experts. However, difficulties arise in determining effectively the framework configuration, i.e., the number of rules, input and output membership functions in a fuzzy system. A fuzzy system design methodology by combining the neural network and fuzzy logic is developed in this paper. The neuro-fuzzy system that can handle both numerical and linguistic data is of a five-layer network. The system not only adaptively adjusts the fuzzy membership functions but also dynamically optimizes the linguistic-fuzzy rules by neural network learning algorithm. It is shown both analytically and experimentally that engineering applications of the neuro-fuzzy system to modeling and control have been very successful.