An extension of the TOPSIS for multi-attribute group decision making under neutrosophic environment

Neutrosophic set theory as a generalization of the fuzzy set theory and intuitionistic fuzzy set theory is an effective tool to deal with inconsistent, imprecise, and vague information. TOPSIS is a multiple attribute method to identify solutions from a finite set of alternatives based upon simultaneous minimization of distance from an ideal point and maximization of distance from a nadir point. In this paper, we first develop a new Hamming distance between single-valued neutrosophic numbers and then present an extension of the TOPSIS method for multi-attribute group decision-making (MAGDM) based on single-valued neutrosophic sets, where the inform ation about attribute values and attribute weights are expressed by decision-makers based on neutrosophic numbers.