混合型多属性决策的灰色关联分析法

针对属性权重信息不完全且属性取值为精确数,区间数和模糊数相结合的混合型多属性决策问题,提出了一种基于理想解的多属性决策的灰色关联分析方法.首先将三种不同形式的属性值均转化为区间数形式,然后依据灰色关联分析的思路,给出了解决该问题的计算步骤,其核心是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对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.

Grey Relational Analysis Method for Hybrid Multiple Attribute Decision Making

For the problem of hybrid multiple attribute decision-making with incomplete information on attribute weights to which the attribute values are given in terms of precision number,interval number and fuzzy numbers,a Grey Relational Analysis(GRA) method is proposed.Firstly,the three different forms of numbers are unified into the form of interval number.Then 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 ideal 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.