Machine learning has recently been widely adopted to address the managerial decision making problems, in which the decision maker needs to be able to interpret the contributions of individual attributes in an explicit form. However, there is a trade-off between performance and interpretability. Full complexity models are non-traceable black-box, whereas classic interpretable models are usually simplified with lower accuracy. This trade-off limits the application of state-of-the-art machine learning models in management problems, which requires high prediction performance, as well as the understanding of individual attributes' contributions to the model outcome. Multiple criteria decision aiding (MCDA) is a family of analytic approaches to depicting the rationale of human decision. It is also limited by strong assumptions. To meet the decision maker's demand for more interpretable machine learning models, we propose a novel hybrid method, namely Neural Network-based Multiple Criteria Decision Aiding, which combines an additive value model and a fully-connected multilayer perceptron (MLP) to achieve good performance while capturing the explicit relationships between individual attributes and the prediction. NN-MCDA has a linear component to characterize such relationships through providing explicit marginal value functions, and a nonlinear component to capture the implicit high-order interactions between attributes and their complex nonlinear transformations. We demonstrate the effectiveness of NN-MCDA with extensive simulation studies and three real-world datasets. To the best of our knowledge, this research is the first to enhance the interpretability of machine learning models with MCDA techniques. The proposed framework also sheds light on how to use machine learning techniques to free MCDA from strong assumptions.