Abstract
Providing partial preference information for multiple criteria ranking or sorting problems results in the indetermination of the preference model. Investigating 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 information. We propose a framework for answering questions regarding stability of these results. In 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 holds. Taking 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 assignment. The improvement or deterioration of the sort of an alternative is quantified with the change of its performances on particular criteria and/or its comprehensive score. The proposed framework is useful in terms of design, planning, formulating the guidelines, or defining the future performance targets. It 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 scores. Application of the proposed approach is demonstrated on the problem of assessing environmental impact of main European cities.
Highlights
The concept of criterion plays a fundamental role in decision aiding
We focus on an additive value function preference model which is of particular interest in Multiple Criteria Decision Aiding (MCDA) for an intuitive interpretation of numerical scores of alternatives and a straightforward impact of pieces of preference information on the final result
Pairwise comparisons When dealing with multiple criteria ranking problems, the basic indirect preference information that may be provided by the Decision Maker (DM) has the form of pairwise comparisons for some reference alternatives
Summary
The concept of criterion plays a fundamental role in decision aiding. Serving as a tool for evaluating and comparing alternatives, a criterion represents a specific point of view on the impact and quality of alternative decisions. While robustness analysis of the obtained recommendations concerned validity of conclusions with respect to allowed changes of either performances or preference model parameters, the post factum analysis extends the concept of such analysis to other useful questions, like “what improvement on all or some performances of a given alternative should be made, so that it achieves a better result in the recommendation obtained with a set of compatible preference models?”, or “what is the margin of safety in some or all performances of a given alternative, within which it can maintain the same rank or class assignment as in the obtained robust recommendation?”.
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