The aim of this paper is to investigate the multiple attribute group decision making(MAGDM) problems with 2tuple linguistic assessment information, in which the information about attribute weights is incompletely known, and the attribute values take the form of linguistic assessment information. In order to get the weight vector of the attribute, we establish two optimization models based on the basic ideal of traditional TOPSIS, by which the attribute weights can be determined. For the special

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... situations where the information about attribute weights is completely unknown, we establish some other optimization models. By solving these models, we get two simple and exact formulas, which can be used to determine the attribute weights. Then, based on the TOPSIS method, calculation steps for solving MAGDM problems with 2-tuple linguistic assessment information are given. The weighted distances between every alternative and 2-tuple linguistic positive ideal solution (TLPIS) and 2-tuple linguistic negative ideal solution (TLNIS) are calculated. Then, according to the weighted distances, the relative closeness degree to the TLPIS is calculated to rank all alternatives. These methods have exact characteristic in linguistic information processing. They avoided information distortion and losing which occur formerly in the linguistic information processing. Finally, some practical examples are used to illustrate the developed procedures.