The aim of this paper is to extend the technique for order preference by similarity to ideal solution (TOPSIS) for solving multiattribute group decision making (MAGDM) problems using Atanassov intuitionistic fuzzy sets (IFSs). In this methodology, weights of attributes and ratings of alternatives on attributes are extracted from fuzziness inherent in decision data and decision making process, and described using Atanassov IFSs. A Euclidean distance measure is developed to calculate the differences between each alternative for each decision maker and an Atanassov IFS positive ideal-solution (IFSPIS) as well as an Atanassov IFS negative ideal-solution (IFSNIS). Degrees of relative closeness to the Atanassov IFSPIS for all alternatives with respect to each decision maker in the group are calculated. Then all decision makers in the group may be regarded as “attributes” and a corresponding classical MADM problem is generated and hereby solved by the TOPSIS. The proposed methodology is validated and compared with other similar methods. A numerical example is examined to demonstrate the implementation process of the methodology proposed in this paper.