Dominance Based Monte Carlo Algorithm for Preference Elicitation in the Multi-criteria Sorting Problem: Some Performance Tests

Abstract

In this article, we study the Dominance Based Monte Carlo algorithm, a model-free Multi-Criteria Decision Aiding (MCDA) method for sorting problems, which was first proposed in Denat and Öztürk (2016). The sorting problem consists in assigning each object to a category, both the set of objects and the set of categories being predefined. This method is based on a sub-set of objects which are assigned to categories by a decision maker and aims at being able to assign the remaining objects to categories according to the decision makers preferences. This method is said model-free, which means that we do not assume that the decision maker’s reasoning follows some well-known and explicitly described rules or logic system. It is assumed that monotonicity should be respected as well as the learning set. The specificity of this approach is to be stochastic. A Monte Carlo principle is used where the median operator aggregates the results of independent and randomized experiments. In a previous article some theoretical properties that are met by this method were studied. Here we want to assess its performance through a k-fold validation procedure and compare this performance to those of other preference elicitation algorithms. We also show how the result of this method converges to a deterministic value when the number of trials or the size of the learning set increases.