| 引用本文: | 朱建军, 刘士新, 王梦光.一种灵敏度和一致性相结合的决策区域分析[J].控制理论与应用,2004,21(4):537~540.[点击复制] |
| ZHU Jian-jun, LIU Shi-xin, WANG Meng-guang.Integration of the sensitivity analysis and consistency analysison the decision making region[J].Control Theory and Technology,2004,21(4):537~540.[点击复制] |
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| 一种灵敏度和一致性相结合的决策区域分析 |
| Integration of the sensitivity analysis and consistency analysison the decision making region |
| 摘要点击 1116 全文点击 1283 投稿时间：2002-11-04 修订日期：2003-09-03 |
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| DOI编号 10.7641/j.issn.1000-8152.2004.4.010 |
| 2004,21(4):537-540 |
| 中文关键词 层次分析法 灵敏度分析 一致性分析 综合决策区域 |
| 英文关键词 analytical hierarchy process sensitivity analysis consistency analysis integration decision making region |
| 基金项目 国家863计划CIMS主题项目(2002AA412010); 辽宁省博士启动基金项目(20021011); 沈阳市自然科学基金项目(1022036-1-04). |
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| 中文摘要 |
| 研究了层次分析法中判断矩阵元素取值对权重排序稳定性和一致性的影响.通过判断矩阵主特征值与特征多项式含三次幂系数之间的负相关关系,导出了使判断矩阵一致性比例最小时元素的最优取值,得到了在该值左侧时判断矩阵一致性单调递减,而在右侧时单调递增的结论,由此设计了迭代算法求出使判断矩阵具有满意一致性时元素的取值范围.并结合保持方案排序不变时的灵敏度分析结果,给出了一个既能保持方案排序不变,又能使判断矩阵符合满意一致性的决策区域.最后给出了进行决策区域分析的一个例子. |
| 英文摘要 |
| The effect of the value of one entry of the comparison matrix on the priority stabilization and consistency ratio in the Analytical Hierarchy Process (AHP) is studied.First,based on the conclusion of the negative correlation between the principal eigenvalue and the coefficient of degree n-3 of the characteristic polynomial of the comparison matrix,the optimization value of the entry that keeps the matrix having the minimum consistency ratio was obtained.The consistency ratio monotonously decreased to the left side of the optimization value,while it monotonously increased to the right side.Second,an iteration algorithm was suggested to find the changeable range of the entry that keeps the matrix having the satisfactory consistency.Third,a decision making region that guaranteed the ranking of the alternative and keeps the matrix having the satisfactory consistency was obtained.Finally,an example was given to illustrate the approach. |
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