A multi-attribute decision-making method based on the third-generation prospect theory and grey correlation degree

Considering the uncertainty of the natural state and the convenience of calculation, based on the third generation prospect theory (3-PT) and grey correlation analysis (GRA), we propose a method to solve the multi-attribute decision-making (MADM) problems where the attributes are described by the linguistic intuitionistic fuzzy numbers (LIFNs). Firstly, we transform the LIFNs into the belief structure that includes identity value and belief degree. Then, the evaluation information represented by belief structure is calculated by using the 3-PT, and the prospect matrix is gotten. The alternatives are ranked by the GRA. Finally, we use the proposed method to calculate an example and compare it with other methods to prove its effectiveness and superiority.