2DLIF-PROMETHEE methods for multiple attribute decision making under 2-dimension linguistic intuitionistic fuzzy environments

In this paper, how to run 2DLIF-PROMETHEE methods are introduced to deal with the multiple attribute decision making (MADM) problems evaluated by 2-dimension linguistic intuitionistic fuzzy variables (2DLIFVs). Firstly, the Euclidean distance and the cosine similarity measures for 2DLIFSs are introduced respectively. Then a hybrid distance for 2DLIFSs is introduced by integrating these two measures. Based on the hybrid distances for 2DLIFSs, six improved preference functions are designed to form the kernel part of 2DLIF-PROMETHEE methods. Finally, the partial ranking order of alternatives or the total ranking order of alternatives may be obtained by 2DLIF-PROMETHEE methods. •Euclidean distance for 2DLIFSs is proposed to measure the difference between two 2DLIFSs.•Cosine similarity for 2DLIFSs is introduced to measure the similarity between two 2DLIFSs.•A hybrid distance for 2DLIFSs is presented by combining the Euclidean distance with the cosine similarity for 2DLIFSs.•Six improved preference functions are developed based on the hybrid distance for 2DLIFSs.•The 2DLIF-PROMETHEE methods are proposed to handle MADM problems.