权重信息不完全的多属性决策的灰色关联分析法

Grey Relational Analysis Method for Multiple Attribute Decision Making with Incomplete Attribute Weights

针对属性权重信息不完全且属性值确定的多属性决策问题,提出了一种灰色关联分析的决策方法.该方法依据一般的灰色关联分析方法的基本思路,给出了解决属性权重信息不完全的多属性决策问题的计算步骤,其核心是通过构建并求解一个单目标最优化模型,得到每个方案与正、负理想方案的关联度,进而计算出每个方案与正理想方案的相对关联度,即可得到所有方案的排序结果.最后给出了一个数值例子,结果表明方法简单,有效和易于计算.

With respect to the problem of multiple attribute decision-maklng with incomplete information on attribute weights to which the attribute values are given in terms of real numbers, a modified Grey Relational Analysis （GRA） method is proposed. The calculation steps to solve it are given. As the key step, a single objective programming model is developed to determine the relation degree between every alternative and positive ideal point or negative ideal point. Then, according to the relation degree, the relative relation degree to the positive point is calculated to rank all alternatives. At last, a numerical example is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.