Decision Analysis with the Set of Normalized Triangular Fuzzy Weight Vectors in Fuzzy AHP
Decision Analysis with the Set of Normalized Triangular Fuzzy Weight Vectors in Fuzzy AHP
复制标题
模糊层次分析法中归一化三角模糊权向量集的决策分析
DOI：
10.1007/978-3-030-98018-4_6
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Masahiro Inuiguchi
中科院分区：
文献类型：
--
作者：
Shigeaki Innan;Masahiro Inuiguchi
在层次分析法(AHP)中引入了区间和模糊数，反映了决策者的模糊性。本文提出了一种用于多准则决策分析的模糊层次分析法。首先，研究了给定模糊成对比较矩阵(PCM)下的归一化模糊权向量估计问题。在回顾了以前的估计问题的方法之后，我们证明了与一致模糊PCM相关的归一化模糊权向量的非唯一性。与相同的一致模糊PCM关联的归一化模糊权向量与给定的PCM的距离相同。因此，我们要求所有这样的模糊权向量都应该是估计问题的解。由于以前的估计方法不能满足这一要求，因此对该估计方法进行了改进，从而估计出所有这些归一化的模糊权向量。然后利用所有这些归一化模糊权向量进行决策分析。用该方法对备选方案的排序范围进行分析时，最优备选方案的稳定性是可以考察的。
Intervals and fuzzy numbers have been introduced to the analytic hierarchy process (AHP) reflecting the vagueness of the decision maker. In this paper, we propose a fuzzy AHP approach to multiple criteria decision analysis. First we investigate the normalized fuzzy weight vector estimation problem under a given fuzzy pairwise comparison matrix (PCM). After reviewing a previous approach to the estimation problem, we show the non-uniqueness of the normalized fuzzy weight vector associated with a consistent fuzzy PCM. Those normalized fuzzy weight vectors associated with the same consistent fuzzy PCM are at the same distance from the given PCM. Therefore, we require that all such fuzzy weight vectors should be the solutions to the estimation problem. As the previous estimation method does not satisfy this requirement, the estimation method is modified so that all such normalized fuzzy weight vectors are estimated. Then a decision analysis with all such normalized fuzzy weight vectors is proposed. The stability of the best alternative can be scrutable as the range of alternative orderings is analyzed by the proposed approach.