Note on diagonal procedure in analytic hierarchy process

We study the paper of Finan and Hurley published in the International Transactions of Operational Research. They created a diagonal procedure in which their comparison matrix is rank-order consistent. The purpose of this paper is fourfold. First, we point out their procedure contains questionable results and improve on them. Second, we show that their procedure cannot guarantee that the consistency index is always less than 0.1. Third, we prove that their method preserves the predetermined rank order. Fourth, we offer a simpler procedure to derive the numerical weights. Hence, we suggest that decision-makers still use the comparison matrix of Saaty. Numerical examples are included to illustrate our findings.