Estimation Methods of Interval Weights Centered at Geometric Mean from a Pairwise Comparison Matrix

Abstract

An interval priority weight estimation method was proposed under the idea that the inconsistency of pairwise comparison matrix comes from human vague evaluation. Because the interval priority weights estimated by the conventional method are often unbalanced and too narrow to represent the vagueness of human judgment, several improved interval priority weight estimation methods have been proposed and shown their better performances by numerical experiments. However, in the numerical experiments on the consistency with the true dominance relation, it is shown that the crisp weights estimated by a method developed in the classical AHP can perform better if we find a proper threshold for utility difference to determine the sure dominance relation. In this paper, with a strong focus on this result, we propose to utilize the geometric mean method developed in the classical AHP for estimation of center values of interval priority weights. The widths of interval priority weights are estimated by several interval priority weight estimation methods developed in our previous studies. The performances of the proposed methods are examined by two kinds of numerical experiments.