Integrated framework for preference modeling and robustness analysis for outranking-based multiple criteria sorting with ELECTRE and PROMETHEE

Abstract

We introduce an integrated framework for preference modeling and robustness analysis in outranking-based multiple criteria sorting. The preference information supplied by the Decision Maker (DM) is composed of parts of desired recommendation and imprecise requirements that the delivered outcomes should satisfy. Its allowed forms are: imprecise assignment examples, desired class cardinalities, and assignment-based pairwise comparisons. The exploitation of all instances of the outranking model compatible with these preferences results in three types of outcomes. These raise robustness concerns in terms of the stability of a suggested assignment for each alternative, an observed size of each class, and a comparison between recommendation delivered for pairs of alternatives. The correspondence between different types of inputs and outputs facilitates the dialogue with the DM and enhances her/his confidence in the suggested recommendation. While referring only to a semantic meaning of an outranking relation, we present the procedures for translating the preference information into parameters of compatible outranking model instances and for deriving various kinds of sorting results. Then, we implement this general framework in the context of outranking models specific for ELECTRE and PROMETHEE. Finally, we show how preference modeling and robustness analysis can be performed and greatly simplified with a set of preference model instances providing precise assignments for the alternatives. The framework proposed for this case is based on Mixed-Integer Linear Programming (MILP), being independent of the underlying model and method. Application of the approaches is demonstrated on the case of classifying Polish research units into four quality classes.