AHP中互反判断矩阵的区间权重确定方法

An Interval Weight Determination Method for Reciprocal Judgment Matrices in AHP

文章借助层次分析法(AHP)中互反判断矩阵的剖分,得到所有可能的完全一致性权重向量,对所有权重向量对应分量,找出最大最小值,从而准确地确定出区间权重向量,并验证所得到的区间权重满足规范化特性。对于较高阶判断矩阵,给出列剖分法近似处理。所给方法克服了常用规划模型的烦琐以及带来偏差的问题,充分显示判断的不一致性波动程度,示例显示了该方法的合理性和有效性。

This paper makes use of the subdivisions of reciprocal judgment matrices in analytic hierarchy process(AHP)to obtain all possible completely consistent weight vectors,and then findsthe maximum and minimum values of the corresponding components of all weight vectors so as to accurately determine the interval weight vector and verify that the obtained interval weight meets the normalization characteristics.Finally,for the judgment matrix of higher order,the paper provides the approximate treatment of column division method.The proposed method overcomes the complexity of common programming models and the problem of deviation,fully showing the inconsistency fluctuation degree of the judgment.An example also shows the rationality and effectiveness of this method.