A new coefficient of rankings similarity in decision-making problems

Abstract

Multi-criteria decision-making methods are tools that facilitate and help to make better and more responsible decisions. Their main objective is usually to establish a ranking of alternatives, where the best solution is in the first place and the worst in the last place. However, using different techniques to solve the same decisional problem may result in rankings that are not the same. How can we test their similarity? For this purpose, scientists most often use different correlation measures, which unfortunately do not fully meet their objective. In this paper, we identify the shortcomings of currently used coefficients to measure the similarity of two rankings in decision-making problems. Afterward, we present a new coefficient that is much better suited to compare the reference ranking and the tested rankings. In our proposal, positions at the top of the ranking have a more significant impact on the similarity than those further away, which is right in the decision-making domain. Finally, we show a set of numerical examples, where this new coefficient is presented as an efficient tool to compare rankings in the decision-making field.