A method is proposed to deal with the uncertain multiple attribute group decision making problems, where 2-dimension uncertain linguistic variables (2DULVs) are used as the reliable way for the experts to express their fuzzy subjective evaluation 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 measure the distance between two 2DULVs. Secondly, two optimization 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 comprehensive evaluation value of each alternative. Then, a score function is used to determine the ranking of the alternatives. Finally, the effectiveness of the proposed method is proved by an illustrated example.

中文翻译：

---

二维不确定语言变量下的多属性群决策方法

提出了一种不确定的多属性群决策问题的处理方法，以二维不确定语言变量（2DULV）为专家表达模糊主观评价信息的可靠方法。首先，为了更准确地测量2DULV，提出了一种比较两个2DULV的新方法，称为得分函数，同时定义了一种新的函数来测量两个2DULV之间的距离。其次，建立了两个优化模型，根据新的距离公式确定专家和属性的权重，并使用加权平均算子确定每个备选方案的综合评估值。然后，使用得分函数来确定备选方案的排名。最后，