A method is proposed to deal with the uncertain mul-tiple attribute group decision making problems,where 2-dimen-sion uncertain linguistic variables (2DULVs) are used as the relia-ble way for the experts to express their fuzzy subjective evalua-tion information.Firstly,in order to measure the 2DULVs more accurately,a new method is proposed to compare two 2DULVs,called a score function,while a new function is defined to mea-sure the distance between two 2DULVs.Secondly,two optimiz-ation models are established to determine the weight of experts and attributes based on the new distance formula and a weighted average operator is used to determine the compre-hensive evaluation value of each alternative.Then,a score func-tion is used to determine the ranking of the alternatives.Finally,the effectiveness of the proposed method is proved by an illus-trated example.