New Directions in Robustness Analysis and Preference Modeling in Multiple Criteria Decision Aiding
We present a set of novel multiple criteria decision aiding (MCDA) methods requiring indirect preference information. They expect the decision maker (DM) to specify some examples of holistic judgments (pairwise comparisons or assignment examples) for reference alternatives which play the role of a training set. Although preference information of this type has been already admitted in some existing methods, we propose innovative mathematical models which allow subsequent induction of compatible values of the preference model parameters. Moreover, we account for preference information which has not received due attention in MCDA research. Precisely, we present new preference disaggregation methods for incorporation of preference information in the form of desired ranks of the reference alternatives in case of ranking problems, and desired cardinalities of classes in case of sorting problems.
When using indirect preference information, there is usually more than one compatible instance of the preference model (i.e. set of model parameters) for which all preference statements provided by the DM are restored. The way of dealing with this indetermination is essential for the final recommendation. We address this problem by extending the principle of robust ordinal regression (ROR), which postulates taking into account all compatible instances of the preference model, rather than a single instance only, as in the traditional MCDA methods.
In particular, we introduce this principle for outranking methods designed for multiple criteria ranking, choice, and sorting problems. Using ROR, these methods build a set of compatible outranking models and define two outranking relations: necessary and possible. We also adapt ROR to multiple criteria group decision, which is among the most important and frequently encountered processes within companies and organizations. Furthermore, we extend ROR for ranking problems with an analysis of extreme results. We consider all rankings that follow the use of the compatible instances of the preference model, and we determine the best and the worst attained ranks and comprehensive scores for each alternative. Finally, we introduce the concept of a representative instance of the preference model. Such an instance is expected to produce a robust recommendation with respect to the non-univocal preference model stemming from input preference information.
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