Robust optimal consensus feedback mechanism with private interest in the context of uncertain cost

During the process of obtaining a consensus, the moderator may recommend modifications based on his personal interests to steer decision-makers (DMs) toward modifying their viewpoints so that the consensus evolves in the desired direction. In the process of revising opinions, the moderator must provide sufficient monetary remuneration to those who are willing to modify their opinions. Nevertheless, there is a lot of uncertainty and both internal and external factors affect the adjustment cost of decision-making. This paper proposes two robust optimal consensus feedback mechanisms with private interests in the context of uncertain cost (UCRFM), taking into account the moderator's private interests and uncertain cost, minimizing the consensus cost under the established consensus threshold, and maximizing the fuzzy consensus measure under the given cost budget. Initially, two types of UCRFMs are presented by employing two uncertainty sets to characterize the uncertain cost, and then two UCRFMs are turned equivalently into a 0-1 programming model. Secondly, based on different uncertainty sets, the corresponding robust counterparts of UCRFMs are constructed to obtain the optimal total consensus cost and the maximum fuzzy consensus. Finally, comprehensive experimental research is conducted to confirm the effectiveness of the proposed approach, and a comparison between the models is given.