基于权重的AHP判断矩阵一致性调整方法
2024,46(1):179-186
耿正霖
国防科技大学 气象海洋学院, 湖南 长沙 410073，oliver8812@163.com.cn
吴佳妮
国防科技大学 气象海洋学院, 湖南 长沙 410073
程兴华
国防科技大学 气象海洋学院, 湖南 长沙 410073
包长春
国防科技大学 气象海洋学院, 湖南 长沙 410073
国防科技大学 气象海洋学院, 湖南 长沙 410073，oliver8812@163.com.cn
吴佳妮
国防科技大学 气象海洋学院, 湖南 长沙 410073
程兴华
国防科技大学 气象海洋学院, 湖南 长沙 410073
包长春
国防科技大学 气象海洋学院, 湖南 长沙 410073
摘要：
传统的判断矩阵调整方法计算得到的权重不能最大限度地保留原始判断矩阵的信息。为此,提出一种基于权重的判断矩阵调整方法。该方法根据权重的性质,构造完全一致矩阵,利用AdaGrad最速下降法对矩阵进行拟合,使该矩阵相对于原始判断矩阵的总改变量最小,以其对应的权重作为矩阵的计算结果。数值计算结果表明,该方法相比于其他方法,权重对原始判断信息的保留度更高,且不需要反复进行矩阵一致性检验。
传统的判断矩阵调整方法计算得到的权重不能最大限度地保留原始判断矩阵的信息。为此,提出一种基于权重的判断矩阵调整方法。该方法根据权重的性质,构造完全一致矩阵,利用AdaGrad最速下降法对矩阵进行拟合,使该矩阵相对于原始判断矩阵的总改变量最小,以其对应的权重作为矩阵的计算结果。数值计算结果表明,该方法相比于其他方法,权重对原始判断信息的保留度更高,且不需要反复进行矩阵一致性检验。
基金项目：
国家自然科学基金资助项目(61702531)
国家自然科学基金资助项目(61702531)
Consistency adjustment method for pairwise comparison matrix in analytic hierarchy process based on weights
GENG Zhenglin
College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China,oliver8812@163.com.cn
WU Jiani
College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China
CHENG Xinghua
College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China
BAO Changchun
College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China
College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China,oliver8812@163.com.cn
WU Jiani
College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China
CHENG Xinghua
College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China
BAO Changchun
College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China
Abstract：
Calculated weights by traditional PCM(pairwise comparison matrix) adjustment methods can′t retain the information of the original PCM to the maximum extent. Therefore, a method for PCM modulation based on the weights was proposed. The method constructed a completely consistent matrix according to the properties of weights, and the matrix was fitted by the AdaGrad method, so as to minimize the total change of the matrix relative to the original PCM. Corresponding weights was taken as the calculation result of the matrix. Numerical results show that this method can significantly improve the retention of original PCM information compared with other methods and does not require repeated consistency checking.
Calculated weights by traditional PCM(pairwise comparison matrix) adjustment methods can′t retain the information of the original PCM to the maximum extent. Therefore, a method for PCM modulation based on the weights was proposed. The method constructed a completely consistent matrix according to the properties of weights, and the matrix was fitted by the AdaGrad method, so as to minimize the total change of the matrix relative to the original PCM. Corresponding weights was taken as the calculation result of the matrix. Numerical results show that this method can significantly improve the retention of original PCM information compared with other methods and does not require repeated consistency checking.
收稿日期：
2021-11-09
2021-11-09
