Abstract: We analyze the stability of scatter degree method, which is one of the most popular comprehensive evaluation methods, from two aspects respectively by considering abnormal object and extreme sample using stochastic simulation method, and then obtain some relevant conclusions. On this basis, we present an improved method for scatter degree method by fusing factor analyzing approach into it. Through the analyses of the stochastic simulation example, we can conclude that this improved method for scatter degree method can weaken the interference of outliers to original data. And then, the numerical example illustrates that the improved method can increase the stability of scatter degree method with the consideration of the internal diversity of a same data group. At last, it is pointed that the scatter degree method applies to the questions with fewer independent indicators, while its improved method based on factor analysis is more suitable to the questions in hierarchical structure with more attributes and belonging to different categories.

Key words: comprehensive evaluation, scatter degree method, stochastic simulation, factor analyzing

摘要： 采用随机模拟仿真的方法分别从增添异常对象和极端样本两个方面对拉开档次法的稳定性进行了分析,给出了相关结论。在此基础上,基于“因子分析”提出了拉开档次法的改进方法,算例部分的分析表明该方法因兼顾了同类数据之间的内部差异,能够削弱“异常值”对原始数据的干扰作用,从而进一步提升了方法的稳定性。最后,指出拉开档次法适用于评价指标数目较少的评价问题,而基于“因子分析”的改进方法则适合于数据数目较多且指标有相关关系的评价问题。

关键词: 综合评价, 拉开档次法, 随机模拟, 因子分析