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针对两类传统的区间主成分分析方法的不足,提出了一种适合综合评价活动的多点区间主成分,并通过数值模拟分析,与既有区间主成分分析方法进行了有效性的比较。结果发现:第一,代表点的增加会增强结论的可靠性,同时,CPCA在整体上优于V-PCA,但在大样本和多指标下V-PCA是更好的选择;第二,在评价活动中,指标较多或样本较大时应选择N-MP-PCA法,而指标较少或小样本下则首选T-MP-PCA法。另外,均匀分布产生的区间数表明N-MP-PCA适合长区间,SG-MP-PCA适合短区间,而正态分布产生的区间数则支持N-MP-PCA适合长区间,T-MP-PCA适合短区间的结论。第三,区间主成分个数及载荷矩阵的产生方式对结论无显著性影响。
Aiming at the deficiency of two traditional methods of interval principal component analysis, a multi-interval interval principal component suitable for comprehensive evaluation activity is proposed and compared with the existing interval principal component analysis method through numerical simulation. The results showed that: First, the increase of representative points will enhance the reliability of the conclusion. Meanwhile, CPCA is superior to V-PCA overall, but V-PCA is the better choice for large sample and multiple indicators. Second, In the evaluation activities, the N-MP-PCA method should be selected when there are more indicators or larger samples, and the T-MP-PCA method is the preferred method with fewer indicators or smaller samples. In addition, the number of intervals generated by uniform distribution shows that N-MP-PCA is suitable for a long interval and SG-MP-PCA is suitable for a short interval, while the number of intervals generated by normal distribution supports N-MP- PCA suitable for short-term conclusions. Third, the number of interval principal components and the generation of load matrix have no significant effect on the conclusion.