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In this paper, we develop some new aggregation operators such as 2-tuple linguistic geometric averaging (TGA) operator, 2-tuple linguistic weighted averaging (TWGA) operator, 2-tuple linguistic ordered weighted geometric averaging (TOWGA) operator and 2-tuple linguistic hybrid geometric averaging (THGA) operator, which can be utilized to aggregate preference information taking the form of linguistic variables, and then study some desirable properties of the operators. Based on the TOWGA and the THGA operators, we propose a practical method for group decision making with linguistic preference relations. The method is straightforward and has no loss of information. Finally, an illustrative example is also given.