Multi-attribute group decision making based on extended TOPSIS method under interval-valued intuitionistic fuzzy environment

In this paper, we propose a novel multi-attribute group decision making (MAGDM) method under interval-valued intuitionistic fuzzy environment by integrating extended TOPSIS and linear programming methods. We assume that multiple decision makers provide the input information, namely the assessment values and attribute weights using interval-valued intuitionistic fuzzy (IVIF) values for incorporating inherent uncertainty in the MAGDM process. Furthermore, the weights of decision makers given by experts to describe their importance in group decision making are assumed as IVIF values. The advantage and disadvantage scores are employed to determine the individual measure of importance for each decision maker. Aggregation of the assessment values and attributes weights are performed using two different IVIF aggregation operators. A weighted similarity measure, based upon the optimal attributes weights obtained through linear programming method, is defined for determining relative closeness coefficients for selection of the most preferred alternative. A real-world case study is provided to illustrate the working of the proposed methodology. Moreover, a thorough comparison has been done with related existing works in order to show the advantages of the methodology.