Interval weight generation approaches for reciprocal relations

In this paper, we propose methods to derive interval weight vectors from reciprocal relations for reflecting the inconsistency when decision makers provide preferences over alternatives (or criteria). Several goal programming models are established to minimize the inconsistency based on multiplicative and additive consistency, respectively. Especially, if we obtain a crisp weight vector from a reciprocal relation, then it is consistent. Then, we extend the proposed methods to incomplete reciprocal relations and interval reciprocal relations and develop the corresponding models to derive interval weight vectors. Several examples are also given to compare the developed methods with the existing ones.