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In multi-criteria decision aiding, the Choquet integral has been used as anaggregation operator to deal with interacting criteria, having as a requirementa prior assumption of common scale for all the criteria. This restriction onthe adopted scale may be considered as a limitation in some practical problems.In order to overcome this limitation, we propose a new Choquet integralformulation, specific for sorting problems, that constructs a common scale fromheterogenous scales using the framework of the FlowSort method. We alsointroduce a new outranking degree based on the Choquet integral preferencemodel, which allows the modeling of interacting criteria in FlowSort.Therefore, the proposed approach can be seen either as an extension of FlowSortfor problems with interacting criteria or as a new Choquet integral formulationfor multi-criteria sorting problems with heterogeneous scales. Numericalexamples attest that the proposed approach is conceptually simple to beimplemented and acknowledge the importance of considering interaction betweencriteria when it exists.

An outranking Choquet integral formulation for multi-criteria sorting  problems with heterogeneous scales: an extension of FlowSort for interacting  criteria