Post factum analysis for robust multiple criteria ranking and sorting

Abstract

Providing partial preference information for multiple criteria ranking or sorting problems results in the indetermination of the preference modelInvestigating the influence of this indetermination on the suggested recommendation, we may obtain the necessary, possible and extreme results confirmed by, respectively, all, at least one, or the most and least advantageous preference model instances compatible with the input preference informationWe propose a framework for answering questions regarding stability of these resultsIn particular, we are investigating the minimal improvement that warrants feasibility of some currently impossible outcome as well as the maximal deterioration by which some already attainable result still holdsTaking into account the setting of multiple criteria ranking and sorting problems, we consider such questions in view of pairwise preference relations, or attaining some rank, or assignmentThe improvement or deterioration of the sort of an alternative is quantified with the change of its performances on particular criteria and/or its comprehensive scoreThe proposed framework is useful in terms of design, planning, formulating the guidelines, or defining the future performance targetsIt is also important for robustness concern because it finds which parts of the recommendation are robust or sensitive with respect to the modification of the alternatives’ performance values or scoresApplication of the proposed approach is demonstrated on the problem of assessing environmental impact of main European cities.