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In the consensus reaching process of group decision making (GDM), consensus measures do not require the consensus opinions of all decision makers. Meanwhile, unit adjustment cost is one of the important and often uncertain factors that affect consensus in GDM. Due to the uncertainty of unit adjustment costs, the moderator may not be able to provide each decision maker with an accurate unit adjustment cost. To overcome these problems, a novel class of group consensus decision models is proposed in this paper. First, fuzzy consensus measures are defined to make the consensus flexible using the specificity and coverage of the consensus granule. Secondly, to describe the uncertainty of the cost of unit adjustment, three uncertainty scenarios are created by the robust optimization approach is introduced. In the end, the feasibility and applicability of the method are verified by taking the classical GDM problem as an example, and sensitivity and comparative analyses are also performed. [ABSTRACT FROM AUTHOR]