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With respect to multiple attribute group decision making (MAGDM) problems in which the attribute weights take the form of interval numbers, and the preference values take the form of uncertain linguistic variables, by utilizing some operational laws of uncertain linguistic variables and a formula for the comparison between two uncertain linguistic variables. A new aggregation operator called interval geometric aggregation (IGA) operator is proposed and then an IGA operator-based approach to MAGDM in uncertain linguistic setting is developed. The approach is simple and effective. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.