Soft computing based on maximizing consensus and fuzzy TOPSIS approach to interval-valued intuitionistic fuzzy group decision making

• We define the consensus index from the perspective of the ranking of decision information and derive the experts’ weights on the basis of the idea of the maximizing consensus.
• We extend the TOPSIS approach to rank all the alternatives from the perspective of the magnitude of decision information under interval-valued intuitionistic fuzzy environment.
• Combining with the multi-choice goal programming models, our approach can not only find the optimal alternative(s) but also determine their corresponding optimum quantities.

Multi-attribute group decision making (MAGDM) is an important research topic in decision theory. In recent decades, many useful methods have been proposed to solve various MAGDM problems, but very few methods simultaneously take them into account from the perspectives of both the ranking and the magnitude of decision data, especially for the interval-valued intuitionistic fuzzy decision data. The purpose of this paper is to develop a soft computing technique based on maximizing consensus and fuzzy TOPSIS in order to solve interval-valued intuitionistic fuzzy MAGDM problems from such two aspects of decision data. To this end, we first define a consensus index from the perspective of the ranking of decision data, for measuring the degree of consensus between the individual and the group. Then, we establish an optimal model based on maximizing consensus to determine the weights of experts. Following the idea of TOPSIS, we calculate the closeness indices of the alternatives from the perspective of the magnitude of decision data. To identify the optimal alternatives and determine their optimum quantities, we further construct a multi-choice goal programming model based on the derived closeness indices. Finally, an example is given to verify the developed method and to make a comparative analysis.

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