AHP中群决策判断矩阵的构造

由于在群决策矩阵的构造时,必须考虑每位专家的意见,又要保持决策矩阵具有AHP中判断矩阵的一般特性。为此,针对层次分析法中群决策的不同专家所建立的判断矩阵,利用不同判断矩阵所对应元素的几何平均法,构造出平均判断矩阵,即群决策判断矩阵。并利用严密的数学方法证明了“所构造的矩阵能保持一致性和满意性”的重要结论。该方法运算简单,不仅为AHP群决策判断矩阵的建立提供了一种有效的方法,而且为群决策的研究提供了一定的理论依据。

Construction of the judgement matrix of group decision-making in AHP

In the costruction of the judgement matrix of group decision-making,because one must consider the different ideas from each expert and keep up that the decision matrix is of the general properity of judgement matrix in AHP.For this purpose,by using the geometry mean method that the product of corresponding factors from the different judgement matrix,for the different judgement matrix built by each expert in the group decision-making,the mean judgement matrix,or the judgement matrix of group decision-making,is built.And the important conclusion is proved that the matrix built can keep up consistency and satisfied consistency by using the strict mathematical method.This technique is simple in operation,and it proposes not only an effective method for the construction of judgement matrix of group decision-making but also a certain theoritical base in the study on group decision-making.