A Concentration Ratio for Nonlinear Best Worst Method

Abstract

Best Worst Method (BWM) is a multi-criteria decision-making method that is based on a structured pairwise comparison system. It uses two pairwise comparison vectors (best-to-others and others-to-worst) as input for an optimization model to get the optimal weights of the criteria (or alternatives). The original BWM involves a nonlinear model that sometimes results in multiple optimal weights meaning that the weight of each criterion is presented as an interval. The aim of this paper is to introduce a ratio, called concentration ratio, to check the concentration of the optimal intervals obtained from the nonlinear BWM. The relationship between the concentration ratio and the consistency ratio is investigated and it is found that the concentration ratio along with the consistency ratio of the model provides enhanced insights into the reliability and flexibility of the results of BWM.