基于正态分布点值化的区间主成分评价法及应用

针对区间数据点值化过程中所存在的“代表性不足”的缺陷，提出了基于正态分布的点值化方法并将之应用于区间主成分评价法。通过与基于中心点值化的区间主成分法的比较，得到三个主要结论：第一，基于正态分布的点值化方法能将各样品的点值化结果导向指标均值，而非区间值的中心点；第二，基于正态分布的点值化结果增加了数据信息量；第三，基于正态分布点值化的区间主成分评价法提高了数据降维效果，具有更好的因子命名能力。应用结果表明，在考虑正态分布情况下，对区间数据的点值化处理方法具有较好的效果，基于正态分布点值化的方法可推广至基于区间数的评价和决策问题。

Interval Principal Component Analysis based on the Point-Estimation of Normal Distribution and its Application

Focusing on the defects of lacking in representation in the process of convert the interval-valued data into point-data,this paper proposes a new method based on normal distribution and applies it into interval-principal component analysis.There are three advantages compared with centers method of principal component analysis for interval-valued data.Firstly,the method of point estimation based on normal distribution can make the point estimation of cases to the mean of index,rather than the midpoint of interval-valued data.Secondly,the data’s point estimation based on normal distribution increases information quantity.Thirdly,interval principal component analysis based on the point estimation of normal distribution enhances the effect of data reduction,and has a better ability to name the factors.The result indicates that the new method can be extended to other methods of comprehensive evaluation or decision making based on interval-valued data.