A complete ranking method for interval-valued intuitionistic fuzzy numbers and its applications to multicriteria decision making

In this study, a complete ranking method for interval-valued intuitionistic fuzzy numbers (IVIFNs) is introduced by using a score function and three types of entropy functions. This work is motivated by the work of Lakshmana Gomathi Nayagam et al. (Soft Comput 21, 7077–7082, 2017) in which a novel non-hesitant score function for the theory of interval-valued intuitionistic fuzzy sets was introduced. The authors claimed that the proposed non-hesitant score function could overcome the shortcomings of some familiar methods. By using some examples, they pointed out that the non-hesitant score function is better compared with Sahin’s and Zhang et al.’s approaches. It is pointed out that although in some specific cases, the cited method overcomes the shortcomings of several of the existing methods mentioned, it also created new defects that can be solved by other methods. The main aim of this study is to give a complete ranking method for IVIFNs which can rank any two arbitrary IVIFNs. At last, two examples to demonstrate the effectiveness of the proposed method are provided.