Abstract: The comparison of linear normalization methods and the conversion method of reverse indicators are important research contents of comprehensive evaluation. From the perspective of internal difference information of indicator, taking TOPSIS, block distance based TOPSIS and linear weighted aggregation method as examples, the frequently used linear normalization methods are compared based on theoretical deduction and empirical analysis, and two conversion methods for reverse indicators are proposed. It is found that for the linear weighted aggregation method and TOPSIS, the difference of normalized range of the same indicator under different linear normalization methods is the key factor leading to the difference of ranking results. In addition, the conversion methods of reverse indicators proposed in this paper can not only ensure that the evaluation values of TOPSIS and block distance based TOPSIS remain unchanged before and after the conversion of reverse indicators, but also realize the equivalence of block distance based TOPSIS and linear weighted aggregation method after the conversion of reverse indicators. Finally, some suggestions for the application of linear normalization methods and conversion methods of reverse indicators are put forward.

Key words: linear normalization method, comparison, reverse indicator, conversion, range

摘要： 线性无量纲化方法的对比及反向指标的正向化方法都是综合评价的重要研究内容。从指标差异信息的角度,以TOPSIS、基于街区距离的TOPSIS和线性加权综合法为例,基于理论推导和实证分析对比了常用的线性无量纲化方法,并提出了两种反向指标正向化方法。研究发现,对于线性加权综合法和TOPSIS,不同线性无量纲化方法下同一指标归一化极差的不同是导致排序结果存在差异的关键因素;本文提出的反向指标正向化方法,不仅可以保证正向化前后TOPSIS、基于街区距离的TOPSIS的评价值不变,也可以实现反向指标正向化后线性加权综合法与基于街区距离的TOPSIS在排序目的上的等效性。最后,本文提出了线性无量纲化方法和反向指标正向化方法的应用建议。

关键词: 线性无量纲化方法, 对比, 反向指标, 正向化, 极差