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Venn Prediction (VP) is a new machine learning framework for producing well-calibrated probabilistic predictions. In particular it provides well-calibrated lower and upper bounds for the conditional probability of an example belonging to each possible class of the problem at hand. This paper proposes five VP methods based on Neural Networks (NNs), which is one of the most widely used machine learning techniques. The proposed methods are evaluated experimentally on four benchmark datasets and the obtained results demonstrate the empirical well-calibratedness of their outputs and their superiority over the outputs of the traditional NN classifier.