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This paper presents an ensemble neural network and interval neutrosophic sets approach to the problem of binary classification. A bagging technique is applied to an ensemble of pairs of neural networks created to predict degree of truth membership, indeterminacy membership, and false membership values in the interval neutrosophic sets. In our approach, the error and vagueness are quantified in the classification process as well. A number of aggregation techniques are proposed in this paper. We applied our techniques to the classical benchmark problems including ionosphere, pima-Indians diabetes, and liver-disorders from the UCI machine learning repository. Our approaches improve the classification performance as compared to the existing techniques which applied only to the truth membership values. Furthermore, the proposed ensemble techniques also provide better results than those obtained from only a single pair of neural networks.