中文摘要：

提出了两个vague值投影和距离的概念，并在此基础上给出了考虑指标权重影响的基于vague集投影和距离的多指标模糊决策方法.在这个方法中，利用候选方案在理想方案上的投影和距离来求出最佳方案.此方法与文献现有的应用vague集相似度度量进行决策的方法相比较，新方法更加合理且弥补了现有方法的不足之处.最后对实例进行分析计算，算例验证了该方法的有效性.

英文摘要：

Conception of distance and projectivity for vague set was presented in this paper. Considering the influence of weight, a weighted decision making method was presented based on vague sets. By calculating the projectivity of vague set for the alternative to the ideal alternative, the best choice was obtained. Compared with the measures of similarity between vague sets given by present articles, this method was rational. This method remedied a defect of present method. At last an example is given, and the example shows that the proposed method is effective.