Multiple attribute decision making (MADM) approaches have been investigated extensively for ranking the alternatives related to multiple attributes. In most existing MADM approaches, attribute weights play a key role due to the fact that the ranking of alternatives may changes with attribute weights vector. Ranking range can be used to measure the lower and upper bounds of all possible rankings of alternatives when attribute weights are varying. In the paper, we investigate the ranking range for the selected seven popular MADM approaches: Weighted averaging (WA), weighted geometric averaging (WGA), ordered weighted averaging (OWA), ordered weighted geometric averaging (OWGA), TOPSIS, PROMETHEE and ELECTRE. Through determining the ranking ranges of alternatives, associated with attribute weights, in the selected seven approaches, we present several desirable properties of the ranking range. Then, we design the simulation experiments with either random or real data to compare the ranking range for selected seven MADM approaches. Interestingly, the experiment results clearly show that TOPSIS$\succ \mathrm{E}\mathrm{L}\mathrm{E}\mathrm{C}\mathrm{T}\mathrm{R}\mathrm{E}\succ$PROMETHEE$~$WA$\succ$WGA$\succ$OWA$\succ$OWGA in the average sense, where '$\succ$' denotes the larger ranking range, and '$~$' denotes no difference in the ranking range. A larger ranking range means an easier to manipulate the ranking of alternatives, and also means a worse robustness of a MADM approach.

已经对多属性决策制定（MADM）方法进行了广泛研究，以对与多属性相关的替代方案进行排名。在大多数现有的MADM方法中，由于替代项的排名可能随属性权重向量而变化，因此属性权重起着关键作用。当属性权重变化时，可以使用等级范围来度量替代方案所有可能等级的下限和上限。在本文中，我们调查了选定的七种流行的MADM方法的排名范围：加权平均（WA），加权几何平均（WGA），有序加权平均（OWA），有序加权几何平均（OWGA），TOPSIS，PROMETHEE和ELECTRE 。通过在所选的7种方法中确定与属性权重相关的替代方案的排名范围，我们介绍了排名范围的一些理想属性。然后，我们使用随机或真实数据设计仿真实验，以比较所选7种MADM方法的排名范围。有趣的是，实验结果清楚地表明TOPSIS$\succ \mathrm{Ë}\mathrm{大号}\mathrm{Ë}\mathrm{C}\mathrm{Ť}\mathrm{[R}\mathrm{Ë}\succ$义卖$〜$西澳$\succ$世界高尔夫协会$\succ$OWA$\succ$从一般意义上讲，OWGA$\succ$'表示较大的排名范围，并且'$〜$'表示排名范围没有差异。较大的排名范围意味着更容易操纵替代方案的排名，也意味着MADM方法的健壮性较差。