Robust elicitation of criteria weights and thresholds in a multicriteria decision aid context
Résumé
Using a multicriteria decision method, and here more specifically an outranking method, to provide a recommendation requires the determination of numerous parameters, such as criteria weights and thresholds. As the final recommendation is strongly dependent on these parameters, it is of the highest importance to avoid impreciseness or to be able to measure their impact on the recommendation. Dealing with an expert decision maker (i.e. having a good a priori knowledge of the problem and his preferences) makes this determination easier and more explicit. However, when dealing with a non-expert decision maker, whose preferences are generally constructed during the decision aid process, it is not possible to directly ask him for some precise parameter values; their determination has to be included in a robust preference elicitation process, taking into account the difficulties and impreciseness.
We extend our earlier work where we defined a mixed integer linear program to determine criteria weights in a robust manner from partial preferential information of the decision maker about pairs of alternatives, in order to recapture the complete median cut outranking relation. This model takes advantage of the Condorcet denotation, which allows characterizing the robustness of the outranking statements towards weights modifications or impreciseness. In an earlier article, we provided a translation of the denotation into mathematical constraints in order to elicit criteria weights by ensuring the best possible robustness to the resulting outranking digraph.
However, tests with real decision makers show that they do not feel at ease when having to fix criteria thresholds. Therefore, we decide to integrate the elicitation of the thresholds in the process. We therefore define a new mathematical model determining simultaneously the criteria weights as well as preference and indifference thresholds, from some decision makers preferential information on pairs of alternatives, keeping in mind the robustness of the resulting outranking digraph. Preliminary tests show that the model only determines discrimination thresholds when necessary, preventing from making false assumptions.
We also develop a second operational tool that determines intervals of stability around each threshold, such that the variation of the threshold inside the interval doesnt involve any change in the median cut outranking digraph. It thus increases the decision makers confidence in the provided thresholds: the bigger is an interval of variation on a threshold, the more robust is the solution towards parameter impreciseness.