Increasing Convergence in Interval Weight Estimations from a Pairwise Comparison Matrix

Abstract

A pairwise comparison matrix (PCM) is often used to estimate the weights of criteria/alternatives. In the conventional methods, a crisp weights have been estimated from a given PCM although the given PCM is not perfectly consistent. Namely, crisp weights are estimated by minimizing the errors. In the interval analytic hierarchy process (interval AHP), weights are estimated by intervals from the point of view that the human conceives interval weights rather than crisp weights in their mind. Because of the insufficiency of the original interval weight estimation method, several alternative estimation methods have been proposed. For such an interval estimation method, the satisfaction of the following properties are preferred: (1) the estimated interval weight vector is normalized, (2) the given PCM is a possible realization under the estimated interval weight vector, (3) the correct crisp weight vector is estimated from the perfectly consistent matrix, and (4) the more PCMs are observed, the closer to the true interval weight vector the estimated interval weight vector comes. Properties (1) to (3) have treated considerably. On the other hand, property (4) has not yet treated so far. In this paper, we propose several estimation methods having properties (1) to (4).