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This paper suggests a uninorm-based neuron model and a neural network architecture using unineurons. The unineuron generalizes logical and/or neurons using weighted uninorms. Previous works have addressed fuzzy neurons within the framework of uninorms. This paper introduces a new unineuron model that uses weighted aggregation of the inputs, and computes its output using a conventional neuron. A feedforward fuzzy neural architecture is developed and used to model nonlinear dynamic systems. The resulting fuzzy neural network easily allows fuzzy rule insertion and/or extraction from its topology, process information following a fuzzy inference mechanism, and is an universal function approximator. Experimental results show that the uninorm-based network provides accurate results and performs better than several similar neural and alternative fuzzy function approximators.