Learning criteria weights of an optimistic Electre Tri sorting rule

Multiple criteria sorting methods assign alternatives to predefined ordered categories taking multiple criteria into consideration. The Electre Tri method compares alternatives to several profiles separating the categories. Based on such comparisons, each alternative is assigned to the lowest (resp. highest) category for which it is at least as good as the lower profile (resp. is strictly preferred by the higher profile) of the category, and the corresponding assignment rule is called pessimistic (resp. optimistic). We propose algorithms for eliciting the criteria weights and majority threshold in a version of the optimistic Electre Tri rule, which raises additional difficulties w.r.t. the pessimistic rule. We also describe an algorithm that computes robust alternatives? assignments from assignment examples. These algorithms proceed by solving mixed integer programs. Several numerical experiments are conducted to test the proposed algorithms on the following issues: learning ability of the algorithm to reproduce the DM?s preference, robustness analysis and ability to identify conflicting preference information in case of inconsistencies in the learning set. Experiments show that eliciting the criteria weights in an accurate way requires quite a number of assignment examples. Furthermore, considering more criteria increases the information requirement. The present empirical study allows us to draw some lessons in view of practical applications of Electre Tri using the optimistic rule.