Integrating incomplete preference estimation and consistency control in consensus reaching

In group decision making (GDM), there exists a situation in which experts may not able to provide comparative judgements regarding all pairs of alternatives, and therefore leading to the expression of incomplete preference. The existing frameworks to manage the GDM problem with incomplete preference relations have been investigated intensively and followed a common resolution scheme composed of three processes: estimation, consistency improvement, and consensus reaching. However, the consensus reaching process is applied after the estimation process and consistency improvement processes, leading to the destruction of the consistency of estimated preference relations, which will duplicate the process of improving consistency and consensus, resulting in significant adjustments of experts' preferences. To avoid this issue, we first propose a joint framework to integrate the consensus reaching process with estimation and consistency improvement. This framework is designed based on a minimum adjustment optimization model with completeness, consistency, and consensus control. It can produce complete preference relations with acceptable consistency and consensus, and simultaneously guarantee the minimum adjustment of experts' preferences. Finally, simulation and comparative analyses are used to justify the validity of the proposal.