Preference disaggregation for multiple criteria sorting with partial monotonicity constraints: Application to exposure management of nanomaterials

We propose a novel approach to multiple criteria sorting incorporating a threshold-based value-driven procedure. The parameters deciding upon the shape of marginal value functions and separating class thresholds are inferred through preference disaggregation from the Decision Maker's incomplete assignment examples and partial requirements on the type of (non-)monotonicity for each marginal value function. These types include standard monotonic shapes, level-monotonic functions, A- and V-types combining increasing and decreasing value trends, and unknown monotonicity constraints. A representative instance of the sorting model compatible with the preference information is constructed by solving a dedicated Mixed-Integer Linear Programming problem. Its complexity is controlled by minimizing the number of changes in monotonicity between all subsequent sub-intervals of marginal value functions. The assignments derived using the constructed representative model are validated against the outcomes of robustness analysis. The proposed method is applied to a real-world problem of exposure management of engineered nanomaterials. We develop a model for predicting precaution level while handling nanomaterials in certain conditions using a respirator. The model captures interrelations between ten accounted evaluation criteria, including both monotonic and non-monotonic criteria, and the recommended class assignment. This makes it suitable for the management of exposure scenarios, which have not been directly judged by the experts.