Multiple attribute decision-making method based on 2-dimension uncertain linguistic density generalized hybrid weighted averaging operator

Two-dimension uncertain linguistic variables (2DULVs) are very effective tools in describing the uncertain and fuzzy information, which are composed of I class linguistic information and II class linguistic information. Density aggregation operators not only consider the importance of all attributes but also take the importance of the density and the order positions of attributes into account, so they can more accurately deal with the fuzzy decision-making problems. In this paper, firstly, some basic theories, such as the definition, the expectation value and the operational laws of the 2DULVs, are briefly introduced. Then, some density aggregation operators based on 2DULVs are proposed, such as 2-dimension uncertain linguistic density arithmetic aggregation operators, 2-dimension uncertain linguistic density geometric aggregation operators and 2-dimension uncertain linguistic density generalized aggregation operators. Furthermore, we propose a multiple attribute decision-making method based on the 2-dimension uncertain linguistic density generalized hybrid weighted averaging operators. Finally, we use an illustrative example to demonstrate the practicality and effectiveness of the proposed method.