成对比较
乘法函数
层次分析法
基质(化学分析)
一致性(知识库)
数学
序数数据
建设性的
有序优化
统计
计算机科学
算法
离散数学
数理经济学
过程(计算)
数学分析
材料科学
复合材料
操作系统
出处
期刊:Symmetry
[MDPI AG]
日期:2021-11-15
卷期号:13 (11): 2183-2183
被引量:6
摘要
The pairwise comparison (PC) matrix is often used to manifest human judgments, and it has been successfully applied in the analytic hierarchy process (AHP). As a PC matrix is formed by making paired reciprocal comparisons, symmetry is a striking characteristic of a PC matrix. It is this simple but powerful means of resolving multicriteria decision-making problems that is the basis of AHP; however, in practical applications, human judgments may be inconsistent. Although Saaty’s rule for the consistency test is commonly accepted, there is evidence that those so-called “acceptable” PC matrices may not be ordinally consistent, which is a necessary condition for a PC matrix to be accepted. We propose an ordinal consistency indicator called SDR (standard deviation of ranks), derive the upper bound of the SDR, suggest a threshold for a decision-maker to assess whether the ordinal consistency of a PC matrix is acceptable, and reveal a surprising fact that the degree of ordinal inconsistency of a small PC matrix may be more serious than a large one. We made a comparative analysis with some other indicators. Experimental results showed that the ordinal inconsistency measured by the SDR is invariant under heterogeneous judgment measurements with a varied spectrum of scales, and that the SDR is superior to the two compared indicators. Note that the SDR not only works for a multiplicative PC matrix but can also be used for additive and fuzzy PC matrices.
科研通智能强力驱动
Strongly Powered by AbleSci AI