模拟研究在AHP中使用的选择不一致性指数之间的关系
1Departments of Mathematics, Czestochowa University of Technology, 42-200 Częstochowa, Poland.
Entropy (Basel, Switzerland)
|October 28, 2023
概括
分析层次过程 (AHP) 是一种多标准决策方法,它使用不一致指数 (ICI) 来检测对对比矩阵中的错误. 一些ICI具有高度相关性,这表明它们可以在AHP分析中互换使用.
科学领域:
- 运营研究 运营研究
- 决策科学 决策科学 决策科学
- 应用数学 应用数学 应用数学
背景情况:
- 分析层次过程 (AHP) 是一种流行的多标准决策方法 (MCDM),依赖于以对对比矩阵 (PCM) 组织的对对比.
- 在PCM中的错误可能会对衍生优先级产生重大影响,需要评估和控制不一致的方法.
- 萨蒂引入了不一致性指数 (ICI) 来识别和管理AHP中的错误,但存在许多定义和变化.
研究的目的:
- 研究分析层次过程 (AHP) 中使用的不同不一致性指数 (ICI) 之间的关系和依赖关系.
- 为了确定某些ICI是否表现出高相关性,表明在实际的AHP应用中潜在的可互换性.
- 通过模拟提供经验证据,证明选定的ICI之间的相关性.
主要方法:
- 使用蒙特卡洛模拟生成数据并观察AHP框架内的依赖关系.
- 选择特定的不一致指数 (ICI) 对进行分析.
- 计算皮尔森相关系数以量化选定ICI之间的线性关联.
- 使用散射图可视化ICI之间的依赖关系.
主要成果:
- 蒙特卡洛模拟显示了某些对不一致指数 (ICI) 之间的显著依赖关系.
- 对于特定的ICI对,观察到高的皮尔森相关系数,表明强有力的线性关系.
- 分散图形在视觉上证实了这些选定的ICI之间的密切相关性.
结论:
- 在分析层次过程 (AHP) 中,一些不一致性指数 (ICI) 具有高度的相关性.
- 这些高度相关的ICI可以在AHP中互换使用,简化决策过程.
- 这些发现有助于更好地了解AHP中不同ICI的行为和关系.
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