一种计算AHP权重的两阶段线性规划方法

对于传统的AHP求解方法,存在难以识别比较矩阵中的不一致判断的情况。通过构造两阶段线性规划模型,在第一阶段求出一致性求解范围,利用该一致性范围作为第二阶段的限制条件,借助于Matlab软件求出了最优的优先权矢量,并举例说明应用这个方法的计算过程。最后,通过具体实例对模型的灵敏性进行了分析,给出了不一致性判断的识别方法。

Two-stage linear programming approach to estimating weights in AHP

It is difficult to locate the inconsistencies among decision maker's judgments in the traditional AHP.Firstly a two-stage linear programming model is presented.In the first stage a linear program that provides a consistency bound for a specified pairwise comparison matrix is formulated.In the second stage the consistency bound is used for a linear program whose solution is a priority vector by means of Matlab.Secondly,a numerical example is given to illustrate the application of this approach.Lastly,the sensitivity analysis is performed on the inputs to the model in a numerical example and a technique is used to detect inconsistency.