层次分析法中随机一致性指标的改进及应用

发布时间：2018-05-26 18:37

本文选题：层次分析法 + 一致性检验　；参考：《海南师范大学》2017年硕士论文

【摘要】：Analytic Hierarchy Process(AHP)方法的局限性在于高阶(15阶以上)的随机一致性指标不够全面,以及传统计算该指标方法的推广能力较弱,理论尚有缺陷。基于此本文给出了在大数据背景下AHP一致性检验中随机一致性指标获取的改进方案,一种是通过构造均匀表的方式设计抽样,得到总体均值的估计;另一种则通过扰动矩阵的分布进行分析,结合分布情况给出符合扰动矩阵分布的蒙特卡罗抽样方法,从而得到了新的随机一致性指标。然后通过不同的数值试验对提出的方案进行了评估和检验,证明了蒙特卡罗抽样方法更为合理有效。最后以新的随机一致性指标为基础,将改进的方法应用于海南岛台风灾害分析问题中,并结合模糊多属性决策理论方法,得到了海南岛台风特性与时空特性的分析结论,不但证明了改进的AHP方法的实用性,也为海南岛台风灾害风险评估提供了理论依据。
[Abstract]:The limitation of Analytic Hierarchy Processing-AHP) method is that the random consistency index is not comprehensive enough, and the generalization ability of the traditional method is weak, and the theory has some defects. Based on this, an improved method of obtaining random consistency index in AHP conformance test under the background of big data is given. One is that sampling is designed by constructing uniform table, and the estimation of population mean is obtained. On the other hand, the distribution of perturbation matrix is analyzed, and the Monte Carlo sampling method according to the distribution of perturbation matrix is given, and a new random consistency index is obtained. Then the proposed scheme is evaluated and tested by different numerical experiments, which proves that the Monte Carlo sampling method is more reasonable and effective. Finally, based on the new random consistency index, the improved method is applied to the typhoon disaster analysis in Hainan Island, and the conclusion of the analysis of typhoon characteristics and space-time characteristics of Hainan Island is obtained by combining the fuzzy multi-attribute decision theory method. It not only proves the practicability of the improved AHP method, but also provides a theoretical basis for typhoon disaster risk assessment in Hainan Island.
【学位授予单位】：海南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O225

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