On Consistency in AHP and Fuzzy AHP
On Consistency in AHP and Fuzzy AHP
复制标题
论层次分析法与模糊层次分析法的一致性
DOI：
10.21078/jssi-2017-128-20
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发表时间：
2017-06
期刊：
影响因子：
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通讯作者：
Witold Pedrycz
中科院分区：
文献类型：
--
作者：
Fang Liu;Yanan Peng;Weiguo Zhang;Witold Pedrycz
摘要层次分析法（AHP）被广泛用于分析各种实际应用中的决策。它的基本思想是将决策问题中遇到的概念构造成一个层次结构，并根据决策者给出的两两比较矩阵来选择最佳方案。在完全理性的经济学假设下，合理的决策应该是一致的。如何分析和保证判断矩阵与决策者判断的一致性成为一个重要的问题。本文件有三个主要目标。首先，我们回顾了定义模糊区间数和三角模糊数的乘性互反矩阵、加性互反矩阵和比较矩阵的一致性和传递性的基本思想和方法。现有的争议背后的应用模糊集理论的层次分析法在文献中。其次，进一步分析了基于AHP和模糊AHP的群决策中集体判断矩阵的一致性问题。指出在模糊层次分析法和群决策中，需要对模糊数偏好关系的弱一致性进行综合研究。第三，考虑到评价过程中的模糊性，提出了AHP中判断矩阵的模糊一致性概念。
Abstract The analytic hierarchy process (AHP) is used widely for analyzing decisions made in various real-world applications. Its basic idea is to construct a hierarchy of concepts encountered in a given decision problem and to choose the best alternative according to pairwise comparison matrices given by the decision maker. Under the assumption of fully rational economics, a reasonable decision should be consistent. It becomes an important issue on how to analyze and ensure the consistency of comparison matrices together with the judgments of the decision maker. The main objectives of the present paper are threefold. First, we review the basic idea and methods used to define the consistency and the transitivity of multiplicative reciprocal matrices, additive reciprocal matrices and comparison matrices with fuzzy interval and triangular fuzzy numbers. The existing controversy behind the applications of fuzzy set theory to the AHP in the literature is presented. Second, the consistency of the collective comparison matrices in group decision making based on AHP and fuzzy AHP is further analyzed. We point out that the weak consistency of preference relations with fuzzy numbers in fuzzy AHP and group decision making should be investigated comprehensively. Third, under the consideration of the vagueness in the process of evaluating the judgements, a new concept of fuzzy consistency of comparison matrices in the AHP is given.
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影响因子：
7
作者：
Zeshui Xu;Qingli Da
通讯作者：
Zeshui Xu;Qingli Da
影响因子：
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作者：
ZADEH, LA
通讯作者：
ZADEH, LA
影响因子：
3
作者：
M. Xia;Jian Chen
通讯作者：
M. Xia;Jian Chen
DOI：
10.1016/b978-1-4832-1450-4.50011-0
发表时间：
1988
期刊：
--
影响因子：
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作者：
R. Yager
通讯作者：
R. Yager
DOI：
10.1049/pbpo161e_ch3
发表时间：
2021-07
期刊：
Artificial Intelligence for Smarter Power Systems: Fuzzy logic and neural networks
影响因子：
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作者：
通讯作者：
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