Tolerance framework for robust group multiple criteria decision making

A tolerance framework is developed to address a group multiple criteria ranking problem with indirect preference information, which is referred to as the interaction, importance and tolerance of criteria as well as pairwise comparisons among alternatives and criteria. Choquet integral preference model is employed to capture the interaction, importance and tolerance of criteria, all of which are specific to decision makers (DMs). Some mandatory/sufficient requirements concerning criteria which are global or local, also called the tolerance attitudes of DMs, are quantified as tolerability constraints. Preference disaggregation analysis is extended to solve this type of tolerability constraints for preference elicitation. Confronted with the inconsistency issue (the feasibility of the whole preference constraints translated from indirect preference information), cause oriented strategy and consequence oriented strategy are established by regression-based mixed 0–1 integer linear programs with the objectives of the most credible minimal inconsistent preference constraints and the most credible maximal preference constraints in the context of group decision making. Considering a wide range of the minimal unsatisfied subsets of preference constraints responsible for the inconsistency and the maximum satisfied subsets of preference constraints as a consistent result, to reach a robust decision, stochastic multicriteria acceptability analysis (SMAA)-like simulation analysis is generated to examine the whole instances of compatible preference models in the modified feasible preference polyhedron and compute the result in a probabilistic form. Simulation experiment is conducted to investigate the influence of global tolerance attitudes of DMs on preference elicitation in conservative and radical scenarios. Finally, the application of the proposed approach to a credit ranking of small and medium-sized enterprises (SMEs) and the comparison analysis with objective methods are presented and discussed for the effectiveness of the proposed tolerance framework.