灰色主成分评价模型的构建及其应用

在梳理和分析主成分分析用于社会科学评价中存在的问题的基础上,将主成分评价拓展到灰色系统领域,构建了灰色主成分评价模型,以灰色相对关联度矩阵代替传统的协方差矩阵或者相关矩阵来进行主成分分析和评价.此外,根据目前主成分评价中权重引起的重复加权问题做一定的讨论,以因子负荷量作为主成分权重合成的重要依据,解决了重要性权对数据的影响问题.最后,构建了两个案例证明所提思想的合理性和有效性.

The construction and application of grey principal component evaluation model

Based on combing the existing problems about applying the principal component analysis into evaluation in social science, the principal component evaluation is extended into the field of grey system and the grey principal component evaluation model is constructed with the grey relative correlation degree matrix instead of the traditional covariance matrix or correlation matrix for principal component analysis and evaluation. In addition, some discussions are done according to the current problem of repeated weight in principal component evaluation, and the factor loading is regarded as important basis of weight synthesis in principal component evaluation, clearing the negative influence of importance weight on data matrix. Finally, two cases are built to show the rationality and validity of the thinking proposed in the article.