Robust minimum cost consensus models with uncertain asymmetric costs based on linear uncertain-constrained tolerance level

The ability of the minimum cost consensus model (MCCM) to promote consensus reaching in the domain of group decision-making (GDM) has been extensively studied. Recently, the MCCM has been enhanced by introducing the consensus principle and tolerance level to achieve a soft consensus. However, the potential impact of asymmetric and uncertain unit adjustment costs on the effectiveness of the consensus reaching process (CRP) has been overlooked. This paper aims to investigate the implications of uncertain asymmetric costs for achieving consensus with a certain level of tolerance, where new robust MCCMs with uncertain asymmetric costs are constructed under four uncertainty sets for the unit adjustment costs. Considering the linear uncertain-constrained tolerance level and consensus level, we incorporate the insight of an expert with a cost-free threshold into models. Additionally, through a pollutant emission application, the proposed robust MCCMs are able to effectively handle uncertainties arising from costs and improve the quality of the CRP compared to the traditional models. Finally, we conduct simulation experiments and sensitivity analysis to illustrate the effectiveness of the proposed models on achieving a consensus by identifying appropriate parameters.