Stochastic ordinal regression for multiple criteria sorting problems

We present a new approach for multiple criteria sorting problems. We consider sorting procedures applying general additive value functions compatible with the given assignment examples. For the decision alternatives, we provide four types of results: (1) necessary and possible assignments from Robust Ordinal Regression (ROR), (2) class acceptability indices from a suitably adapted Stochastic Multicriteria Acceptability Analysis (SMAA) model, (3) necessary and possible assignment-based preference relations, and (4) assignment-based pair-wise outranking indices. We show how the results provided by ROR and SMAA complement each other and combine them under a unified decision aiding framework. Application of the approach is demonstrated by classifying 27 countries in 4 democracy regimes.