An extended TOPSIS method for multiple attribute decision making problems with unknown weight based on 2-dimension uncertain linguistic variables

An extended TOPSIS method is proposed to solve the multiple attribute decision making problems in which the attribute values take the form of 2-dimension uncertain linguistic variables and the attribute weight is unknown. Firstly, the operational rules of 2-dimension uncertain linguistic variables are established and the related features are studied, and the distance formula of 2-dimensional uncertain variables is proposed. Then, the attribute weight can be calculated by utilizing the maximum deviation method, and ranking the order of the alternatives is done by TOPSIS method. Finally, an illustrate example is given to show the decision making steps and the effectiveness of this method.