Interval-valued intuitionistic fuzzy MADM method based on TOPSIS and grey correlation analysis

In this paper, we propose an interval-valued intuitionistic fuzzy Multi-Attribute Decision Making (MADM) method based on improved TOPSIS and Grey Correlation Analysis (GCA), in which the attribute values are interval-valued intuitionistic fuzzy numbers. So that we can deal with imprecise information in fuzzy and rough form in MADM problems by using interval-valued intuitionistic fuzzy numbers Firstly, the concept of interval intuitionistic fuzzy entropy is introduced to calculate the entropy weight of attributes. And the combined weight is calculated by combining the entropy weight with the subjective weight. Secondly, the reverse order phenomenon in the traditional TOPSIS method is eliminated by constructing absolute Positive Ideal Solution (PIS) and absolute Negative Ideal Solution (NIS) in the form of interval-valued intuitionistic fuzzy numbers. Furthermore, the improved TOPSIS method and grey correlation analysis method are combined to describe the degree of closeness for each alternative from the ideal solution, and then the ranking and selection of each alternative are made accordingly to this degree. Finally, the rationality and effectiveness of our method are verified by an example and its sensitivity analysis. The result shows that our method makes the solution of MADM problems more objective and reasonable.