Analysis and comparison of two methods for improving consistency of judgement matrix

Methods for improving consistency of judgement matrix in the analytic hierarchy process are studied. The convergence of the weighted arithmetic mean method for improving consistency of judgement matrix is proven, and the comparison between the weighted arithmetic mean method and the weighted geometric mean method is also given in detail. Theoretical analysis shows that both methods converge and can be used to improve the judgement matrix. However, the weighted geometric mean method is simpler than the weighted arithmetic mean method, and the former can keep the reciprocity of the improved judgement matrix without transformation. The numerical results also indicate that the weighted geometric mean method needs fewer iterations than the weighted arithmetic mean method.