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Type-2 fuzzy set and type-2 intuitionistic fuzzy set are important tools for dealing with problems involving uncertainty and linguistic variables. However, it is sometimes difficult to model problems involving inconsistent data by using these approaches. In this paper, the concept of type-2 single-valued neutrosophic sets is defined in order to cope with this difficulty. Also, some distance measure methods for type-2 single-valued neutrosophic sets based on Hausdorff, Hamming and Euclidean distances are introduced and some properties of them are investigated. Furthermore, a multi-criteria group decision-making method is developed based on TOPSIS approach under the type-2 single-valued neutrosophic environment. Finally, an illustrative example is given in order to show the validity and process of the proposed method.