A MIP-based approach to learn MR-Sort models with single-peaked preferences

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) consists in computing MR-Sort parameters that match a dataset. Existing learning algorithms for Inv-MR-Sort consider monotone preference on criteria. We extend this problem to the case where the preference on criteria are not necessarily monotone, but possibly single-peaked (or single-valley). We propose a mixed-integer programming based algorithm that learns from the training data the preference on criteria together with the other MR-Sort parameters. Numerical experiments investigate the performance of the algorithm, and we illustrate its use on a real-world case study.