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Fuzzy system has been known to provide a framework for handling uncertainties and imprecision by taking linguistic information from human experts. However, difficulties arise in determining effectively the fuzzy system configuration, i.e., the number of rules, input and output membership functions. A neuro-fuzzy system design methodology by combining neural network and fuzzy logic is developed in this paper to adaptively adjust the fuzzy membership functions and dynamically optimize the linguistic-fuzzy rules. The structure of a five-layer feedforward network is shown to determine systematically the correct fuzzy logic rules, tune optimally (in the sense of local region) the parameters of the membership functions, and perform accurately the fuzzy inference. It is shown both numerically and experimentally that engineering applications of the neuro-fuzzy system to vibration control have been very successful.

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