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This article focuses on the membership-mismatched impulsive exponential stabilization for fuzzy unconstrained multilayer neural networks (MNNs) with node-dependent time-varying delays (NDTVDs). To begin with, this work proposes a novel MNNs model with unconstrained interlayer and intralayer parameters, which may allow nodes in all layers to have inconsistent attributes and structures. Meanwhile, the novel model considers the NDTVDs and removes the strict constraints including node alignment and one-to-one interlayer connection to meet diverse modeling requirements in complex applications. Then, the proposed fuzzy impulsive controller does not need to share the same fuzzy parameters as the fuzzy MNNs model, reducing the implementation complexity of the fuzzy impulsive controller. To derive the main results using the augmented vector form of unconstrained MNNs, the sparse matrix method is proposed to convert the node-dependent delayed MNNs model into an equivalent model with multiple delays. Moreover, the time-dependent Lyapunov function (TDLF) technique is adopted to improve the reliability of the stabilization conditions by fully utilizing the state information of both the current and neighboring impulsive intervals. Finally, the main results are verified using numerical simulation.