Liver transplantation is a promising and widely-accepted treatment for patients with terminal liver disease. However, transplantation is restricted by the lack of suitable donors, resulting in significant waiting list deaths. This paper proposes a novel donor-recipient allocation system that uses machine learning to predict graft survival after transplantation using a dataset comprised of donor-recipient pairs from the King's College Hospital (United Kingdom). The main novelty of the system is that it tackles the imbalanced nature of the dataset by considering semi-supervised learning, analysing its potential for obtaining more robust and equitable models in liver transplantation. We propose two different sources of unsupervised data for this specific problem (recent transplants and virtual donor-recipient pairs) and two methods for using these data during model construction (a semi-supervised algorithm and a label propagation scheme). The virtual pairs and the label propagation method are shown to alleviate the imbalanced distribution. The results of our experiments show that the use of synthetic and real unsupervised information helps to improve and stabilise the performance of the model and leads to fairer decisions with respect to the use of only supervised data. Moreover, the best model is combined with the Model for End-stage Liver Disease score (MELD), which is at the moment the most popular assignation methodology worldwide. By doing this, our decision-support system considers both the compatibility of the donor and the recipient (by our prediction system) and the recipient severity (via the MELD score), supporting then the principles of fairness and benefit. (C) 2017 Elsevier B.V. All rights reserved.