Abstract: This paper discusses a multi-attribute decision-making problem of Vague set，which attribute values and preference values are Vague values.Aiming at the fact that attribute values and preference values on alternatives expressed by Vague values are transferred into intuitionistic fuzzy values，attribute weight is obtained by building and solving a programming model，which uses the deviations existed between attribute values and preference values on alternatives expressed by intuitionsitic fuzzy values，it analyzes irrationality of programming modeling built in related reference.By minimizing the deviations between synthesizing values and preference values on alternatives expressed by intuitionistic fuzzy numbers，attribute weight is obtained by building and solving a programming model.By transforming Vague sets into fuzzy sets，it obtains fuzzy matrix and the fuzzy priority relation matrix by using linear ranking of fuzzy matrix，and by cutting the fuzzy priority relation matrix，the best alternative can be obtained.A practical example is given to illustrate the feasibility of the developed method.

Key words: multi-attribute decision-making, Vague set, intuitionistic fuzzy numbers, attribute weight

摘要： 研究了方案属性值和偏好值均为Vague值的多属性决策问题。针对相关文献中，将由Vague值表示的方案属性值与偏好值转化为直觉模糊数，并根据直觉模糊数表示的方案属性值与偏好值之间的偏差建立规划模型并求解属性权重这一过程，分析了建立的规划模型的不合理性。提出通过最小化直觉模糊数表示的方案综合值与偏好值的偏差，建立并求解一个规划模型计算属性权重的改进方法。通过将Vague值转化为模糊值，利用模糊值矩阵的线性序构造模糊优先矩阵，并对其进行分割，从而实现方案的排序择优。通过一个实例说明了该方法的可行性。

关键词: 多属性决策, Vague集, 直觉模糊数, 属性权重