MULTIMOORA-Sort: A Multi-Criteria Sorting Framework Integrating Criteria Interactions, Explanations, and Preference Disaggregation

Multi-criteria sorting methods are widely used to classify alternatives into ordinal categories based on multiple criteria, which frequently arise in various real-world scenarios. Most existing approaches, however, address compensatory, non-compensatory, or dependent effects separately, overlooking their potential coexistence and interaction in practice. To address this limitation, we propose MULTIMOORA-Sort, a novel multi-criteria sorting approach that unifies these effects using the principle of multiplicative multi-objective optimization by ratio analysis (MULTIMOORA). To reduce the decision-maker’s cognitive burden of parameter specification and subjective uncertainty, we develop preference disaggregation analysis (PDA) framework to infer model parameters from assignment examples. Additionally, to enhance trust and interpretability, we introduce a counterfactual explanation framework that illustrates how changes in performance across criteria affect category assignments. The effectiveness of the proposed MULTIMOORA-Sort is demonstrated through two applications: (i) classifying 180 countries by economic freedom using indirect elicitation via PDA, and (ii) assessing the global health security status of 195 countries using direct elicitation. Results show that MULTIMOORA-Sort successfully unifies diverse decision behaviors, supports parameter learning, and provides intuitive explanations of sorting outcomes, offering a robust framework for practical multi-criteria sorting decision-making.