Compressed Air Energy Storage (CAES) is an energy storage method that utilizes compressed air to store energy underground and releases it when needed. In recent years, with the increasing demand to address the variability of renewable energy, research and application of CAES technology have gradually become a focus in the energy field. The stability of underground artificial caverns for compressed air energy storage has always been a key research priority, and its influencing factors are relatively complex, making the establishment of a reasonable risk evaluation system urgently needed. To investigate the stability of underground artificial caverns for CAES and establish a reasonable comprehensive risk evaluation system, the Analytic Hierarchy Process (AHP) and entropy method were introduced to determine comprehensive weights, combined with a mathematical model of the fuzzy comprehensive evaluation method. First, the stability indicator system for underground artificial caverns was established. Based on the AHP and entropy method, weights were assigned to each evaluation indicator to obtain comprehensive weights. On the basis of extensive literature research and numerical simulations, risk levels for each evaluation indicator were classified. Then, combined with the fuzzy mathematics evaluation method, the fuzzy matrix for each evaluation indicator was determined. By integrating the fuzzy matrix of each evaluation indicator with the comprehensive weights, the comprehensive evaluation results for the underground artificial cavern gas storage were obtained. This model was applied to validate a representative test cavern, and the evaluation results were consistent with actual conditions, demonstrating the method's accuracy and its potential to provide valuable insights for engineering practices.