Most of the extant studies in social recommender system are based on explicit social relationships, while the potential of implicit relationships in the heterogeneous social networks remains largely unexplored. This study proposes a new approach to designing a recommender system by employing grey relational analysis on the heterogeneous social networks. It starts with the establishment of heterogeneous social networks through the user-item bipartite graph, user social network graph and user-attribute bipartite graph; and then uses grey relational analysis to identify implicit social relationships, which are then incorporated into the matrix factorization model. Five experiments were conducted to test the performance of our approach against four state-of-the-art baseline methods. The results show that compared with the baseline methods, our approach can effectively alleviate the sparsity problem, because the heterogeneous social network provides richer information. In addition, the grey relational analysis method has the advantage of low requirements for data size and efficiently relieves the cold start problem. Furthermore, our approach saves processing time, thus increases recommendation efficiency. Overall, the proposed approach can effectively improve the accuracy of rating prediction in social recommendations and provide accurate and efficient recommendation service for users.

社会推荐系统中现存的大多数研究都是基于显式的社会关系，而异构社会网络中隐性关系的潜力在很大程度上仍未得到开发。这项研究提出了一种通过对异构社交网络进行灰色关联分析来设计推荐系统的新方法。首先通过用户项目二分图，用户社交网络图和用户属性二分图建立异构社交网络。然后使用灰色关联分析来识别隐式的社会关系，然后将其纳入矩阵分解模型。进行了五个实验，以针对四种最先进的基线方法测试我们的方法的性能。结果表明，与基线方法相比，我们的方法可以有效地缓解稀疏性问题，因为异构的社交网络可提供更丰富的信息。另外，灰色关联分析方法具有对数据大小要求低的优点，并有效地缓解了冷启动问题。此外，我们的方法节省了处理时间，从而提高了推荐效率。总体而言，所提出的方法可以有效地提高社交推荐中的评级预测的准确性，并为用户提供准确而有效的推荐服务。我们的方法节省了处理时间，从而提高了推荐效率。总体而言，所提出的方法可以有效地提高社交推荐中的评级预测的准确性，并为用户提供准确而有效的推荐服务。我们的方法节省了处理时间，从而提高了推荐效率。总体而言，所提出的方法可以有效地提高社交推荐中的评级预测的准确性，并为用户提供准确而有效的推荐服务。