A new decision-making approach for multiple criteria sorting with an imbalanced set of assignment examples

We propose a novel approach to address a multiple criteria sorting (MCS) problem with an imbalanced set of assignment examples. The approach employs a piecewise-linear additive value function as the preference model and adopts the disaggregation-aggregation paradigm to infer a sorting model from provided assignment examples on a set of reference alternatives. We utilize a hierarchical clustering algorithm and several linear programming models to identify reference alternatives that are active to develop the sorting model, so that inactive ones are eliminated from the whole set of reference alternatives. Then, in order to construct a balanced set of assignment examples, a balancing algorithm is proposed to balance active reference alternatives across categories. Finally, the sorting model is obtained by minimizing the sum of violations between values of active reference alternatives and corresponding category thresholds. Furthermore, the performance of the proposed approach is investigated on a hypothetical problem and several real data sets. The experimental results show that our approach is efficient to address the MCS problem with an imbalanced set of assignment examples.