Interval Weight Estimation Methods Satisfying Desirable Properties in Interval AHP

Abstract

From the viewpoint that the inconsistency of a pairwise comparison matrix comes from the vagueness of decision maker’s evaluation, interval AHP representing the vagueness as interval weights was proposed. It has been shown that the interval weight vector estimated by the conventional estimation method does not reflect the vagueness well. Several alternative estimation methods have been proposed. However, those methods do not always satisfy the following desirable properties while the conventional method does: (0) the method is parameter-free, (i) the given pairwise comparison matrix is realizable under the estimated interval weight vector, (ii) the unique accurate crisp weight vector is estimated under a consistent crisp pairwise comparison matrix, (iii) the estimated interval weight vector satisfies the normality condition and (iv) a proper interval weight vector is estimated from a consistent interval pairwise comparison matrix. In this paper, we show that the previous alternative estimation methods do not satisfy some of those properties and propose novel interval weight estimation methods satisfying those five requirements. The non-uniqueness of optimal normalized interval weight vector is also taken care in this paper.