The rapid development of intelligent algorithms has significantly expanded the range of algorithms available for Prognostics and Health Management (PHM). Selecting the appropriate algorithm for a specific task is crucial for effective PHM applications. Learning from past PHM cases is an effective way to automate algorithm recommendations, reducing reliance on expert experience. Human-AI collaboration provides new ideas for achieving this capability. However, in emerging fields or early-stage research, the limited number of cases—coupled with volatility and noise—often results in low recommendation accuracy and weak stability. To address this issue, we propose a multi-order random graph convolution network (MOR-GCN) within a case-learning paradigm. This method uses graphs to model and optimize case correlations, helping engineers narrow down algorithm choices to suitable candidates. We first develop a correlation modeling and optimization method based on a graph network, enhancing information aggregation between similar cases and reducing the impact of case noise on the recommendation model. Next, we design an ensemble recommender using MOR-GCN, which aggregates features of adjacent case nodes through a case correlation network graph (CCNG), further improving recommendation accuracy and stability through ensemble learning. Experimental results from a gearbox fault diagnosis case set demonstrate that the MOR-GCN model can automatically recommend fault diagnosis algorithms based on task attributes, achieving an average accuracy of 77.20 % for single recommendations and 89.90 % for fuzzy recommendations. This framework showcases the potential of artificial intelligence (AI) to assist human decision-making in PHM, minimizing the dependency on expert knowledge during the PHM design stage.