区间数多指标决策问题的新灰色关联分析法

New method of grey relational analysis to multiple attribute decision making with intervals

针对属性权重和属性值均为区间数的多属性决策问题,提出了一种新的灰色关联分析法。首先定义了区间数正理想方案,由此计算出各方案相对于正理想方案的区间数灰色关联系数。然后运用区间数的数乘运算和加法运算计算出各方案相对于正理想方案的关联度,并利用一种对区间数排序的方法,比较各方案的关联度来确定方案的优劣。给出了一个数例,证明所提方法简单、有效,易于实现。

With respect to multiple attribute decision-making problem in which both the attribute weights and attribute values are interval numbers, a new method of grey relational analysis （GRA） is proposed. Firstly, the definition of positive ideal solution of multiple attribute decision-making problem with interval numbers is given, and by which the grey relational coefficient of alternatives from the positive ideal solution is drived. Secondly, the grey relational degrees of alternatives are obtained by using the scale-multiplication and addition operations of interval numbers. The priority of alternative is determined by comparing the grey relational degree intervals of alternatives based on a ranking approach of the interval numbers. At last, a numerical example is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to implement.