Learning MR-Sort Models from Non-Monotone Data
This work addresses the inverse MR-Sort problem for decision-makers in multi-criteria sorting, but it is incremental as it extends existing methods to handle non-monotone preferences.
The authors tackled the problem of learning MR-Sort models from data with non-monotone preferences, such as single-peaked or single-valley criteria, by proposing a mixed-integer programming algorithm. They demonstrated its performance through numerical experiments and a real-world case study, though no concrete numbers were provided in the abstract.
The Majority Rule Sorting (MR-Sort) method assigns alternatives evaluated on multiple criteria to one of the predefined ordered categories. The Inverse MR-Sort problem (Inv-MR-Sort) computes MR-Sort parameters that match a dataset. Existing learning algorithms for Inv-MR-Sort consider monotone preferences on criteria. We extend this problem to the case where the preferences on criteria are not necessarily monotone, but possibly single-peaked (or single-valley). We propose a mixed-integer programming based algorithm that learns the preferences on criteria together with the other MR-Sort parameters from the training data. We investigate the performance of the algorithm using numerical experiments and we illustrate its use on a real-world case study.