梯度特征向量排序法的数学原理

§1 梯度特征向量排序法关于层次分析中,单一准则下的排序问题,Saaty教授提出了特征向量排序法.即决策者在准则C下,对n个需要排序的对象填写判断矩阵:

梯度特征向量排序法（GEM）新元素导入时的保序性原理

梯度特征向量排序法，导出的判断矩阵Ａ提供的排序信息基本上反映在Ａ的上三角元素中，因此我们决定利用上三角判断矩阵来研究在单一准则下新元素增加时的保序性原理。

判断矩阵一致性检验的新方法

给出了两种通用的判断矩阵一致性检验方法的理论依据和利用该指标的统计检验方法以及该一致性检验方法的有关性质和数值计算例子

Multi-attribute decision-making based on subjective and objective integrated eigenvector method

An integrated approach is proposed to investigate the fuzzy multi-attribute decision-making （MADM） problems, where subjective preferences are expressed by a pairwise comparison matrix on the relative weights of attributes and objective information is expressed by a decision matrix. An eigenvector method integrated the subjective fuzzy preference matrix and objective information is proposed. Two linear programming models based on subjective and objective information are introduced to assess the relative importance weights of attributes in an MADM problem. The simple additive weighting method is utilized to aggregate the decision information, and then all the alternatives are ranked. Finally, a numerical example is given to show the feasibility and effectiveness of the method. The result shows that it is easier than other methods of integrating subjective and objective information.