Grey relational bidirectional projection method based on trapezoidal type-2 intuitionistic fuzzy numbers

Intuitionistic fuzzy number, which is an extension of fuzzy number, has been applied in many fields as it considers membership degree and non-membership degree. However, in some circumstances, intuitionistic fuzzy number does not express uncertainty and vagueness well. In order to deal with this problem, a new concept of trapezoidal type-2 intuitionistic fuzzy number(TrT2IFN) is proposed in this paper. Meanwhile, the arithmetical operations of TrT2IFNs are defined. Then, a novel distance measures are proposed by taking advantage of the Hausdorff distance. Additionally, the multi-attributes decision making problem of the TrT2IFN is solved by the grey relational bidirectional projection method. Finally, the applicability and availability of the proposed method are demonstrated by a numerical example, and the final ranking outcome of alternatives is obtained. This paper provides an effective solution for solving multi-attribute decision making in TrT2IFN environment.