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Extensive uncertainty can affect the efficiency and fairness of consensus in the consensus reaching process (CRP), but few scholars have studied consensus modeling that focuses on fairness and efficiency in uncertain environments. Additionally, the weight of the decision maker (DM) in the CRP is influenced by multiple factors. Therefore, this paper proposes robust consensus models (EFCMs) focusing on fairness and efficiency under uncertain costs to address these issues. Firstly, this paper constructs multiple uncertainty sets to describe the uncertainty of the unit adjustment cost. Secondly, the fair utility level and opinion adjustment distance are used to measure the fairness and efficiency of reaching consensus, respectively. Furthermore, this paper uses a data-driven method based on the KDE method combined with trust propagation in social networks to determine the DMs' weights jointly. Finally, this paper also applies the proposed models to the carbon emission reduction negotiation process between the government and enterprises. The experimental results and sensitivity analysis show that the consensus cost budget and the DMs' jealous preference behavior particularly affects the efficiency of reaching consensus, which provides a theoretical basis for solving practical decision making problems. [ABSTRACT FROM AUTHOR]