The aggregation operators based on the 2-dimension uncertain linguistic information and their application to decision making

With respect to 2-dimension uncertain linguistic variables, we improve the operational rules of them by transferring the II class uncertain linguistic variables into intuitionistic fuzzy numbers during the process of calculation. It is able to void omitting information and to make the operations more accurate. Firstly, the operational laws of 2-dimension uncertain linguistic information are improved, and their characteristics are proved. Then, 2-dimension uncertain linguistic weighted averaging (2DULWA) operator, 2-dimension uncertain linguistic weighted geometric (2DULWG) operator and 2-dimension uncertain linguistic generalized weighted average (2DULGWA) operator are proposed by new operational laws aforementioned, and some properties and special cases of these operators are discussed. Furthermore, based on the 2DULGWA operator, an approach to the multiple attribute group decision making with 2-dimension uncertain linguistic variables is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.