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The multivalued neuron with periodic activation function (MVN-P) was proposed by Aizenberg for solving classification problems. The boundaries between two distinct categories are crisply specified in MVN-P, which may result in slow convergence or being unable to converge at all in the learning process. In this paper, we propose a revised model of MVN-P based on the idea of unsharp boundaries. In this revised model, a fuzzy buffer is provided around a boundary between two distinct categories, allowing incorrect assignments with membership degree less than a threshold to be tolerated in the training phase. Genetic algorithms are applied to derive optimal values for the parameters involved in this model, alleviating the burden of setting them manually by the user. Besides, MVN-P has difficulties solving the classification problems having a large number of categories. A tree structure is developed to overcome these difficulties. Simulation results demonstrate the effectiveness of our proposed ideas. [ABSTRACT FROM AUTHOR]