Convergence performance of several interval weight estimation methods under a given pairwise comparison matrix

Abstract

Human evaluations are often vague and the evaluation values cannot always be precisely expressed by real numbers. On the other hand, the preference information is not sufficient to build the mathematical model of the preference accurately. In this paper, we consider interval weight estimation methods which estimate the evaluation values by intervals reflecting the vague human perception of object evaluation, and investigate their adequacy. Assume true interval weights, the estimation method with high estimation accuracy is preferred. However, the highly performed estimation method is not always useful when more preference information is available. Namely, the convergence to the true interval weights with increasing preference information cannot be guaranteed. We give estimation methods which estimate the true interval weights accurately from the perfectly correct interval pairwise comparison matrix, and examine their convergence performances by numerical experiments.