A geometric approach for ranking interval-valued intuitionistic fuzzy numbers with an application to group decision-making

•An approach for ranking interval-valued intuitionistic fuzzy number is developed.•The suggested methodology has obvious geometric meaning.•The developed method can also compare any two intervals.•The established model has been successfully applied to group decision-making.

The ranking of interval-valued intuitionistic fuzzy numbers (IVIFNs) is very important for fuzzy decision-making problems. This paper presents a geometric approach for ranking IVIFNs. Based on the technique for order performance by similarity to an ideal solution, this method is applied to group decision-making in an intuitionistic fuzzy environment. First, all individual decisions with IVIFNs are aggregated into a collective decision. Next, the ideal solutions of collective decision are established. Then the alternatives are ranked based on the geometric method presented in this paper. The practicability, feasibility and effectiveness of the proposed method is illustrated by an experimental analysis.