Learning the Parameters of a Multiple Criteria Sorting Method

Multicriteria sorting methods aim at assigning alternatives to one of the predefined ordered categories. We consider a sorting method in which categories are defined by profiles separating consecutive categories. An alternative

a

is assigned to the lowest category for which

a

is at least as good as the lower profile of this category, for a majority of weighted criteria. This method, that we call MR-Sort, corresponds to a simplified version of ELECTRE Tri. To elicit the values for the profiles and weights, we consider a learning procedure. This procedure relies on a set of known assignment examples to find parameters compatible with these assignments. This is done using mathematical programming techniques.

The focus of this study is experimental. In order to test the mathematical formulation and the parameters learning method, we generate random samples of simulated alternatives. We perform experiments in view of answering the following questions: (a) assuming the learning set is generated using a MR-Sort model, is the learning method able to restore the original sorting model? (b) is the learning method able to do so even when the learning set contains errors? (c) is MR-Sort model able to represent a learning set generated with another sorting method, i.e. can the models be discriminated on an empirical basis?