Estimating relative importance of criteria by post-processing dominance-based rough set approach's outputs

The dominance-based rough set approach (DRSA) is one of the rare multicriteria sorting methods that does not require a priori values for the relative importance of criteria. This method therefore is cognitively less demanding. However, the decision-maker may lack some valuable information that is needed to explain and justify final decisions to stakeholders. The relative importance of criteria can instead be estimated based on the characteristics of the outputs of the DRSA, which are mainly decision rules and attribute reducts. The estimated values can then be used to understand the role played by each criterion and justify the final decisions to stakeholders. This paper first reviews and improves the decision rule attractiveness measure and the relative importance measures that are based on decision rules and attribute reducts, which were all proposed in the authors' previous work. It also introduces new measures that rely on the marginal contributions and entropy of the criteria. This paper also extends these measures to estimate the relative importance of criteria with respect to specific unions of classes. The proposed measures have been applied to Brexit referendum and bankruptcy risk assessment datasets. Both applications showed that the proposed measures generally lead to different results. This can be explained by the diversity of the knowledge on which these measures rely and also by the multiplicity of the analytical perspectives associated with them. The results also showed that the marginal contribution-based measure is a good estimator of both Shapley and Banzhaf values.