Prioritisation in the analytic hierarchy process for real and generated comparison matrices

This study presents a comparison of six popular prioritisation methods in the analytic hierarchy process. The additive normalisation, eigenvector, logarithmic least squares, weighted least squares, fuzzy preference programming, and cosine maximisation methods are compared by assessing their performance on hundreds of randomly generated and real-life pair-wise comparison matrices taken from publications in international journals. The analysis is based on two evaluation criteria, namely, the Euclidean distance and the order reversal criterion (also known as the minimum violation criterion). In addition, the Manhattan distance criterion (also known as conformity) is used to indicate the difference in the priority vectors derived by individual methods from aggregated vectors for all methods. The evaluation procedure uses a full range of inconsistent pair-wise comparison matrices with three to nine dimensions. The results show that the cosine maximisation method outperforms the other methods concerning the Euclidean distance criterion. Most of the methods exhibit similar performance concerning the minimum violation criterion. The logarithmic least squares method produces the priority vector that in the majority of all matrices is closer (conformity indicator) than the others to the aggregated reference priority vector.