Fuzzy analytic hierarchy process (FAHP) has been extensively applied to multi-criteria decision making (MCDM). However, the computational burden resulting from the calculation of fuzzy eigenvalue and eigenvector is heavy. As a result, a FAHP problem is usually solved using approximation techniques such as fuzzy geometric mean (FGM) and fuzzy extent analysis (FEA) instead of exact methods. Therefore, the FAHP results are subject to considerable inaccuracy. To solve this problem, in this study, a FAHP method based on the combination of α -cut operations (ACO), center-of-gravity (COG) defuzzification and defuzzification convergence mechanism (DCM) is proposed. First, ACO is applied to derive the near-exact fuzzy maximal eigenvalue and fuzzy weights. Subsequently, the α cuts of the fuzzy maximal eigenvalue and fuzzy weights are interpolated to generate samples that are uniformly distributed along the x -axis so that COG can be correctly applied to defuzzify the fuzzy maximal eigenvalue and fuzzy weights. To accelerate the computation process, DCM is applied to terminate the enumeration process if the defuzzified values of fuzzy weights have converged. The ACO–COG–DCM method has been applied to a real case to illustrate its applicability. In addition, a simulation study was also conducted to perform a parametric analysis. According to the experimental results, the proposed ACO–COG–DCM method improved the accuracy of estimating fuzzy weights by up to 56%. Furthermore, the experimental results also showed that the inaccuracy of estimating fuzzy weights was mostly owing to the deficiency of the FAHP method rather than the inconsistency of fuzzy pairwise comparison results.