Dominance based monte carlo algorithm for preference learning in the multi-criteria sorting problem: Theoretical properties

In this article we study a new model-free Multi-CriteriaDecision Aiding (MCDA) method for sorting problems where ob-jects are assigned to predefined and ordered categories. The problemthat we deal is the following: given a learning set of objects definedon multi-attributes and already assigned by the decision maker, howto find the assignments of the remaining objects. Being model-free,we do not assume that the decision maker’s reasoning follows somewell-known and explicitly described rules or logic system. We onlyassume that monotonicity should be respected as well as the learningset. The specificity of our approach is to be probabilistic. A MonteCarlo principle is used where the median operator aggregates the re-sults of independent and randomized experiments. We proved thatour final sortings respect the monotonicity and the learning set andthe aggregation with the median operator converges almost surely.nonouirechercheInternationa