2DLIF-PROMETHEE based on the hybrid distance of 2-dimension linguistic intuitionistic fuzzy sets for multiple attribute decision making. (15th September 2022) - Zhu, Hua; Zhao, Jianbin
Abstract: 2-dimension linguistic intuitionistic fuzzy set (2DLIFS) includes two classes of linguistic intuitionistic fuzzy variables, which has a more powerful and flexible ability in representing and handling uncertainty than 2-dimension linguistic fuzzy set (2DLFS) and intuitionistic fuzzy set (IFS). Distance and similarity are two important tools to quantify the difference and closeness of 2DLIFSs. This paper proposes the Euclidean distance and the cosine similarity measures for 2DLIFSs, respectively. Due to the limitation of the Euclidean distance and the cosine similarity measures for 2DLIFSs, a hybrid distance for 2DLIFSs is introduced by integrating these two measures. Further, based on the hybrid distance for 2DLIFSs, 2DLIF-PROMETHEE methods are introduced to deal with the multiple attribute decision making (MADM) problems under 2DLIF environment. Finally, a numerical example is provided to demonstrate the advantages and practicality of 2DLIF-PROMETHEE methods. Highlights: Euclidean distance for 2DLIFSs is proposed to measure the difference of 2DLIFSs. Cosine similarity for 2DLIFSs is introduced to measure the similarity of 2DLIFSs. A hybrid distance for 2DLIFSs is presented by combining the above two measures. Six improved functions are proposed based on the hybrid distance for 2DLIFSs. The 2DLIF-PROMETHEE methods are developed to handle MADM problems.