Robust stochastic sorting with interacting criteria hierarchically structured

In this paper we propose a multiple criteria decision aiding method to deal with sorting problems in which alternatives are evaluated on criteria structured in a hierarchical way and presenting interactions. The underlying preference model is the Choquet integral, while the hierarchical structure of the criteria is taken into account by applying the Multiple Criteria Hierarchy Process. Considering the Choquet integral based on a 2-additive capacity (non additive weights for considered criteria), we present a procedure to find all minimal sets of pairs of interacting criteria representing the preference information provided by the Decision Maker (DM). Robustness concerns are also addressed applying the Robust Ordinal Regression and the Stochastic Multicriteria Acceptability Analysis. Even if in different ways, both of them provide recommendations on the hierarchical sorting problem at hand by exploring the whole set of capacities compatible with the preferences provided by the DM. The applicability of the considered method to real world problems is demonstrated by an example regarding rating of European countries evaluated on economic, governmental and financial data provided by Standard & Poor's Global Inc.