An ordinal regression approach for multicriteria decision support with interacting criteria

The construction of Multi-Attribute Value Theory (MAVT) models in Multiple Criteria Decision Analysis is particularly challenging when interactions between criteria are present. While additive aggregation models are widely accepted due to their transparency and intuitive interpretation, they impose restrictive independence assumptions. In contrast, multilinear models allow for modeling interactions, but pose greater complexity in the elicitation and explanation of preference parameters. This paper proposes a new disaggregation methodology based on the Segmenting Description approach, adapted to multilinear aggregation models, enabling the representation of interactions between pairs of criteria that are meaningful to the decision-maker. The computational challenges of the Segmenting Description approach are taken into account through the integration of redundant-constraint detection techniques that enhance efficiency. To address variability and imprecision in the elicitation of partial value functions, we introduce a structured robustness analysis framework based on the generation of multiple scenarios and the use of the Hit-and-Run method, enabling a more thorough exploration of the decision space and more robust recommendations. Additionally, we propose a non-linear Robust Ordinal Regression approach tailored to multilinear MAVT models with interactions between pairs of criteria, which explicitly distinguishes between partial value functions, weights, and interaction parameters. When multiple compatible models exist, we introduce a process to identify a representative value function or to refine the feasible region based on the preferences of the decision-maker. The proposed contributions aim to enhance transparency, scalability, and interpretability of MAVT applications with interacting criteria.