灰色关联投影下的模糊多属性群决策方法

Fuzzy multi-attribute group decision making method based on grey relation projection

针对属性评价信息为区间直觉梯形模糊数的多属性群决策问题,给出一种基于灰色关联投影的群决策方法。在规范化处理各决策矩阵的基础上,定义负极端决策矩阵及平均决策矩阵,根据各决策矩阵与这两类矩阵的距离大小确定决策者权重,由区间直觉梯形模糊数加权算术平均算子及决策者权重得到群体决策矩阵。由各方案与正、负理想方案的相对贴近度最小化确定各属性权重,以正理想方案为参考,计算各方案与参考序列关于每个属性的灰色关联系数,并计算各方案到正理想方案的灰色关联投影值,根据各方案投影值大小实现对方案的排序择优。将所给群决策方法应用到生鲜冷库空调系统选择决策问题中,算例分析的过程体现了该群决策方法有效性与可行性。

With respect to multi-attribute group decision making problem with interval-valued intuitionistic trapezoidalfuzzy assessment information, a grey relation-projection method is proposed. On the basis of standardized decision matrixes,negative extreme decision matrix and average decision matrix are defined according to the distance between every decisionmatrix and two types of decision matrices, decision maker weights are determined. Group decision matrix is determinedbased on decision-maker weights and interval-valued intuitionistic trapezoidal fuzzy number weighted arithmeticaveraging operator. Basing on the minimization of relative similarity degree between each alternative and the positive(ornegative)ideal alternative to get attribute weights, the positive ideal alternative is seen as the reference sequence, greyrelational coefficient of attributes between each alternative and positive ideal alternative, grey relation-projection of everyattributes to positive ideal alternative. A ranking of alternatives is determined by projected values of the alternatives. Finally,the selection decision problem of air conditioning system of frozen storage is given to illustrate the effectiveness and feasibilityof the proposed method.