The eigenvector method is one of the most used methods for deriving priorities of objects from multiplicative pairwise comparison matrices in Analytic Hierarchy Process (AHP). Fuzzy extension of AHP has been of much attention in order to capture uncertainty stemming from subjectivity of human thinking and from incompleteness of information that are integral to multi-criteria decision-making problems. Various fuzzy extensions of the eigenvector method have been introduced in order to derive fuzzy priorities of objects from fuzzy multiplicative pairwise comparison matrices. These fuzzy extensions are critically reviewed in this paper, and it is showed that (i) they violate multiplicative reciprocity of the related pairwise comparisons, (ii) they are not invariant under permutation of objects, (iii) the fuzzy maximal eigenvectors are not normalized, or (iv) a given normalized fuzzy maximal eigenvector does not consist of normalized maximal eigenvectors obtainable from multiplicative pairwise comparison matrices forming the fuzzy multiplicative pairwise comparison matrices. Afterwards, a new fuzzy extension of the eigenvector method based on the constrained fuzzy arithmetic is introduced and it is shown that it satisfies all four desirable properties.

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从模糊乘法成对比较矩阵中导出归一化模糊优先级的模糊特征向量法

特征向量法是在层次分析法（AHP）中从成对的成对比较矩阵推导对象优先级的最常用方法之一。为了捕获由于人类思维的主观性和多准则决策问题必不可少的信息不完整所引起的不确定性，层次分析法的模糊扩展一直备受关注。为了从模糊乘法成对比较矩阵中得出对象的模糊优先级，引入了特征向量方法的各种模糊扩展。本文对这些模糊扩展进行了严格的审查，结果表明：（i）它们违反了相关成对比较的乘法可逆性；（ii）在对象置换下它们不是不变的；（iii）模糊最大特征向量未归一化，或（iv）给定的归一化模糊最大特征向量不包括可从形成模糊乘法成对比较矩阵的成对成对比较矩阵中获得的归一化最大本征向量。然后，引入了一种基于约束模糊算法的特征向量方法的新模糊扩展，证明了它满足了所有四个理想的性质。