对方案有偏好的模糊多属性决策的GRA方法

Grey relational analysis method for triangular fuzzy number-based multiple attribute decision making with preference information on alternatives

针对属性权重信息不完全且属性值和对方案的主观偏好信息均以三角模糊数形式给出的多属性决策问题,提出了一种基于灰色关联分析GRA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,给出了解决该问题的计算步骤,其核心是通过构建并求解一个单目标最优化模型,通过求解该模型得到属性权重信息,从而得到每个方案客观偏好值对主观偏好值的灰色关联系数,进而计算出每个方案客观偏好与主观偏好的关联度,根据关联度对所有方案进行排序。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 multiple attribute decision making problems in which the attribute weight infor- mation is incomplete and the attribute values and subjective preference values are triangular fuzzy numbers, the method of grey relational analysis （GRA） is proposed for triangular fuzzy number-based multiple attribute deci- sion making with preference on alternatives. Then the calculating steps to solve it are given. As the key step, a single objective programming model is constructed to obtain the attribute weights. The relational coefficients be- tween objective preference and subjective preference of every alternative are obtained. According to the relation- al degree, all alternatives are ranked. Finally, a numerical example is provided to illustrate the proposed meth- od. The result shows the approach is simple, effective and easy to calculate.