Vincent Mousseau

Pegdwende Minoungou, Vincent Mousseau, Wassila Ouerdane et al.

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.

K. Belahcène, C. Labreuche, N. Maudet et al.

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 a NCS model based on a learning set. Exact approaches based on mixed integer linear programming ensures 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 about the inferred model. In this paper, we propose an alternative formulation to learn a 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 more efficient than existing exact MIP approaches.

Olivier Sobrie, Nicolas Gillis, Vincent Mousseau et al.

Additive utility function models are widely used in multiple criteria decision analysis. In such models, a numerical value is associated to each alternative involved in the decision problem. It is computed by aggregating the scores of the alternative on the different criteria of the decision problem. The score of an alternative is determined by a marginal value function that evolves monotonically as a function of the performance of the alternative on this criterion. Determining the shape of the marginals is not easy for a decision maker. It is easier for him/her to make statements such as "alternative $a$ is preferred to $b$". In order to help the decision maker, UTA disaggregation procedures use linear programming to approximate the marginals by piecewise linear functions based only on such statements. In this paper, we propose to infer polynomials and splines instead of piecewise linear functions for the marginals. In this aim, we use semidefinite programming instead of linear programming. We illustrate this new elicitation method and present some experimental results.

K. Belahcene, C. Labreuche, N. Maudet et al.

Multicriteria decision analysis aims at supporting a person facing a decision problem involving conflicting criteria. We consider an additive utility model which provides robust conclusions based on preferences elicited from the decision maker. The recommendations based on these robust conclusions are even more convincing if they are complemented by explanations. We propose a general scheme, based on sequence of preference swaps, in which explanations can be computed. We show first that the length of explanations can be unbounded in the general case. However, in the case of binary reference scales, this length is bounded and we provide an algorithm to compute the corresponding explanation.