Selection of a representative sorting model in a preference disaggregation setting: A review of existing procedures, new proposals, and experimental comparison

We consider preference disaggregation in the context of multiple criteria sorting. The value function parameters and thresholds separating the classes are inferred from the Decision Maker's (DM's) assignment examples. Given the multiplicity of sorting models compatible with indirect preferences, selecting a single, representative one can be conducted differently. We review several procedures for this purpose, aiming to identify the most discriminant, average, central, parsimonious, or robust models. Also, we present three novel procedures that implement the robust assignment rule in practice. They exploit stochastic acceptabilities and maximize the support given to the resulting assignments by all feasible sorting models. The performance of fourteen procedures is verified on problem instances with different complexities. The results of an experimental study indicate the most efficient procedures in terms of classification accuracy, reproducing the DM's model, and delivering the most robust assignments. These include approaches identifying differently interpreted centers of the feasible polyhedron and robust methods introduced in this paper. Moreover, we discuss how the performance of all procedures is affected by different numbers of classes, criteria, characteristic points, and reference assignments.& COPY; 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This article discusses preference disaggregation in the context of multiple criteria sorting. The value function parameters and thresholds separating different classes are inferred from the Decision Maker's assignment examples. Different procedures for selecting a representative sorting model are reviewed, and three novel procedures implementing the robust assignment rule are presented. Experimental results show that the most efficient procedures in terms of classification accuracy, reproducing the DM's model, and delivering robust assignments include approaches identifying differently interpreted centers of the feasible polyhedron and the robust methods introduced in this paper. The impact of different numbers of classes, criteria, characteristic points, and reference assignments on the performance of all procedures is also discussed.