Ranking alternatives expressed with interval-valued intuitionistic fuzzy set

Interval-valued intuitionistic fuzzy (IVIF) set (IV-IFS) is effective in dealing with fuzziness and uncertainty inherent in decision data derived from decision maker and the actions performed in multi-attribute decision making (MADM). Therefore, in this paper, we investigate the MADM problems with uncertain attribute weight information in the framework of IVIFS. We first propose a new accuracy function for solving the problem of ranking alternatives expressed with IVIFSs. Secondly, we propose a linear-programming decision making method based on the accuracy function to solve the MADM problem with binding attribute weight information conditions under IVIF environment. Thirdly, we present an entropy-based decision making method based on the accuracy function to deal with the MADM problem with completely unknown attribute weights under IVIF environment. Finally, two supplier selection examples are given to demonstrate the feasibility and validity of the proposed MADM methods, by comparing it with other fuzzy MADM methods.