The sharing economy has promoted the rapid development of the global economy, the stable matching plays a vital role in resource sharing. However, the large-scale platform increases the difficulties of stable matching, like low efficiency and weak matching. To realize stable and efficient matching in a large-scale platform, our study designs a recurrent neural network-multiple criteria decision aiding (RNN–MCDA) method. Firstly, to avoid time-consuming mutual assessment in large-scale matching, the RNN–MCDA method is proposed to learn and predict the demanders’ and suppliers’ (DAS) uncertain preferences, like linguistic preferences, which are frequently used in sharing platforms. Considering the disadvantages of low accuracy and interpretability in predicting linguistic preferences in previous studies, we combine the RNN and MCDA to learn and predict the linguistic preferences of DAS. Then, for the matching mechanism, to realize the stable matching, we design a two-stage matching mechanism based on RNN–MCDA. At the first stage, we aim at maximizing total satisfaction based on RNN–MCDA instead of inefficient mutual assessment. For the second stage, we focus on the individuals who do not meet the stable constraint in the first stage and use the platforms’ strategies to adjust the satisfaction of DAS and realize stable matching. Finally, an improved cuckoo algorithm is designed to solve the bi-level programming. An example in the manufacturing capacity sharing platform is used to verify our study.