To address complexity information fusion problems involving fuzzy and grey uncertainty information, we develop prioritized averaging aggregation operator and Bonferroni mean aggregation operator with grey linguistic 2-tuple variables and apply them to design a new decision-making scheme. First, the grey linguistic 2-tuple prioritized averaging operator is developed to characterize the prioritization relationship among experts and employed to fuse experts’ information into an overall opinion. Second, we establish dual generalized grey linguistic 2-tuple weighted Bonferroni mean operator to capture the interrelationship among (...) any attribute subsets, which can be reduced to some conventional operators by adjusting parameter vector. On that basis, a flexible group decision-making approach with fuzzy and grey information is designed and applied to an evaluation problem, in which grey relationship analysis method and a linear programming model are combined to extract attribute weights from partially known attribute information. Furthermore, an illustrative example is employed to illustrate the practicality and flexibility of the designed method by conducting the related comparative studies. (shrink)