| 层次分析法中判断矩阵一致性修正的新算法 |
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| 引用本文： | 张桂清,陈义华.层次分析法中判断矩阵一致性修正的新算法[J].数学的实践与认识,2009,39(23). |
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| 作者姓名： | 张桂清 陈义华 |
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| 作者单位： | 重庆大学数理学院,四川,重庆,400044 |
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| 摘 要： | 设计了判断矩阵一致性修正的一种新方法,使判断矩阵一致性在每次迭代修正过程中得到最大程度改善,并通过一个非线性规划模型描述每次迭代的过程.同时作者也证明了这种迭代方法具有收敛性,即通过有限次迭代能够达到满意的一致性阈值.最后给出了一个算例,并进行了比较.
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| 关 键 词： | 层次分析法 判断矩阵 一致性 |
A New Method for Improving the Consistency of the Comparison Matrix in AHP |
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| ZHANG Gui-qing,CHEN Yi-hua.A New Method for Improving the Consistency of the Comparison Matrix in AHP[J].Mathematics in Practice and Theory,2009,39(23). |
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| Authors: | ZHANG Gui-qing CHEN Yi-hua |
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| Abstract: | We proposed a nonlinear programming model for improving the consistency of comparison matrix, by which the consistency ratio value of the modified matrix is less than that of the original one. Then a genetic simulated annealing algorithm was designed to solve the nonlinear programming model. At last we gave an algorithm to derive a positive reciprocal matrix with acceptable consistency, and then the convergence theorem for the given algorithm is established. Numerical calculation examples show that the presented model is more feasible and effective. |
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| Keywords: | the analytic hierarchy process Comparison Matrix consistency |
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