Interval weight generation approaches based on consistency test and interval comparison matrices

A simple yet pragmatic method of consistency test is developed to check whether an interval comparison matrix is consistent or not. Linear programming method is used to derive consistent interval weights from consistent interval comparison matrices and to aggregate local interval weights to generate global interval weights. In cases where an interval comparison matrix is inconsistent, an eigenvector method-based nonlinear programming (NLP) approach is developed to generate interval weights that can meet pre-determined consistency requirements. A simple and effective preference ranking method is utilized to compare the interval weights of criteria or rank alternatives. Three numerical examples including a hierarchical (AHP) decision problem are provided to illustrate the validity and practicality of the proposed methods.