Consensus reaching in group decision making with linear uncertain preferences and asymmetric costs

Abstract

Consensus reaching process (CRP), as an essential part of group decision making (GDM), can facilitate more effective consensus by taking human behaviors into account. Extending the established research on uncertain minimum cost consensus models (MCCMs), this article continues to adopt linear uncertainty distributions (LUDs) to represent decision-maker’s (DM’s) preference, but considers asymmetric costs into a new framework of CRP, where DM’s preference and weight are both adjusted according to democratic consensus. Moreover, in light of the uncertain distance measure, two novel optimization-based consensus models are built in this article: one is to obtain a minimum cost consensus by simultaneously considering asymmetric costs, aggregation function, and consensus measure; while the other provides a more flexible way to address GDM problems without presetting a specific consensus level (CL) threshold. Some 0–1 binary variables are further introduced to reduce the calculation complexity resulted from piecewise functions in the new multicoefficient goal programming models. Finally, an illustrative example and further discussion reveal the feasibility and superiority of our new method.