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In this paper, we extend TOPSIS (technique for order preference by similarity to ideal solution) by three approaches to aggregating group preferences, in order to solve multiple attribute decision analysis (MADA) problems in the situation of belief group decision making (BGDM), where the attribute evaluation of each decision maker (DM) is represented by the bba (basic belief assignment), the applied foundation of Dempster-Shafer theory (DST). Corresponding to three approaches, three extended TOPSIS models, the premodel, the postmodel, and the intermodel, are elaborated step by step, which are used to find solutions to BGDM. In three extended models, the aggregation of group preferences depends on some rules of evidence combination, some social choice functions, and some mean approaches, respectively. Furthermore, a numerical example clearly illustrates the procedures of three extended models for BGDM.