Deriving the fuzzy priorities of criteria from pairwise comparison results is a challenging task in fuzzy multi-criterion decision-making problems. Most past work accomplishes this task by estimating the values of fuzzy priorities or fitting the membership functions of fuzzy priorities using alpha-cut operations (ACO). The former is error-prone, while the latter is time-consuming. To address these issues, this study proposes an efficient approximating ACO (exACO) method by incorporating two novel treatments. First, both logarithmic and exponential functions are used to approximate the membership functions of fuzzy priorities. Second, the enumeration process in ACO is monitored and terminated if the α cuts of fuzzy priorities converge. The proposed methodology has been applied to two cases in the literature. According to the experimental results, the exACO method reduced the average estimation error by 80% while increasing the computational efficiency by 98%. The contribution of this study is to accurately derive fuzzy priorities while maintaining high computational efficiency.