Parameter-Free Interval Priority Weight Estimation Methods Based on Minimum Conceivable Ranges Under a Crisp Pairwise Comparison Matrix

Abstract

Methods for interval priority weight estimation from a crisp pairwise comparison matrix were proposed in the interval analytic hierarchy process assuming the vagueness of human evaluation. The interval priority weights estimated by the conventional method do not reflect the intrinsic vagueness in the given pairwise comparison matrix (PCM). This paper proposes parameter-free methods based on minimal conceivable ranges for estimating interval priority weights from a crisp pairwise comparison matrix. The estimated interval priority weight vectors are required to satisfy (1) the potential reproducibility, (2) the normality, and (3) the preservation of the perfect consistent data. Estimation methods of interval priority weights are proposed based on the minimum possible range. We show those proposed methods satisfy the required three properties. The estimation problem of interval priority weights potentially has multiple solutions with which the associated interval PCMs are identical to one another. To make the further investigation simpler, we use an interval priority weight vector among multiple solutions such that the sum of the center values of interval priority weights is one. We compare the estimation methods of interval priority weights from the viewpoint of estimation accuracy by numerical experiments. Namely, by generating crisp pairwise comparison matrices randomly under true interval PCMs, we evaluate the accuracies of the estimated interval priority weight vectors by comparing the true interval priority weight vectors.