An efficient SAT formulation for learning multiple criteria non-compensatory sorting rules from examples

The literature on Multiple Criteria Decision Analysis (MCDA) proposes several methods in order to sort alternatives evaluated on several attributes into ordered classes. Non-Compensatory Sorting models (NCS) assign alternatives to classes based on the way they compare to multicriteria profiles separating the consecutive classes. Previous works have proposed approaches to learn the parameters of an NCS model based on a learning set. Exact approaches based on mixed integer linear programming ensure that the learning set is best restored, but can only handle datasets of limited size. Heuristic approaches can handle large learning sets, but do not provide any guarantee that the inferred model is the one that best matches the input data. In this paper, we propose an alternative formulation to learn an NCS model. This formulation, based on a SAT problem, guarantees to find a model fully consistent with the learning set (whenever it exists), and is computationally much faster than existing exact MIP approaches.