On the one hand, artificial neural networks (ANNs) are commonly labelled as black-boxes, lacking interpretability; an issue that hinders human understanding of ANNs' behaviors. A need exists to generate a meaningful sequential logic of the ANN for interpreting a production process of a specific output. On the other hand, decision trees exhibit better interpretability and expressive power due to their representation language and the existence of efficient algorithms to transform the trees into rules. However, growing a decision tree based on the available data could produce larger than necessary trees or trees that do not generalise well. In this paper, we introduce two novel multivariate decision tree (MDT) algorithms for rule extraction from ANNs: an Exact-Convertible Decision Tree (EC-DT) and an Extended C-Net algorithm. They both transform a neural network with Rectified Linear Unit activation functions into a representative tree, which can further be used to extract multivariate rules for reasoning. While the EC-DT translates an ANN in a layer-wise manner to represent exactly the decision boundaries implicitly learned by the hidden layers of the network, the Extended C-Net combines the decompositional approach from EC-DT with a C5 tree learning algorithm to form decision rules. The results suggest that while EC-DT is superior in preserving the structure and the fidelity of ANN, Extended C-Net generates the most compact and highly effective trees from ANN. Both proposed MDT algorithms generate rules including combinations of multiple attributes for precise interpretations for decision-making.