Multiple attribute decision making (MADM) is used to rank the alternatives according to evaluation information based on multiple attributes, and many MADM methods have been studied to deal with the MADM problems. In existing MADM methods, when setting different attribute weights, the ranking of alternatives are different. And ranking range can be used to measure a lower bound and an upper bound of rankings of alternatives with the change of the attribute weights. Also, in some real MADM problems, the information on attribute weights may be unknown or partially known, which is called incomplete attribute weight information. Then, this study investigates the ranking range models (RRMs) under incomplete attribute weight information in the selected six MADM methods: Weighted geometric averaging (WGA), Ordered weighted geometric averaging (OWGA), TOPSIS, VIKOR, PROMETHEE and ELECTRE. Particularly, we can construct several 0-1 mathematical programming models to compute the ranking range of alternatives under incomplete attribute weight information for the selected six MADM methods. Then, two case studies on project investment and Academic Ranking of World Universities (ARWU) are used to justify the validity of the RRMs under incomplete attribute weight information in the selected six MADM methods.

中文翻译：

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选取的六种MADM方法在不完全属性权重信息下的排序范围模型

多属性决策（MADM）用于根据基于多属性的评估信息对备选方案进行排序，并且已经研究了许多MADM方法来处理MADM问题。在现有的 MADM 方法中，当设置不同的属性权重时，备选方案的排名是不同的。排序范围可以用来衡量属性权重变化时备选方案排序的下限和上限。此外，在一些实际的 MADM 问题中，属性权重的信息可能是未知的或部分已知的，称为不完整的属性权重信息。然后，本研究在选定的六种 MADM 方法中研究了不完全属性权重信息下的排序范围模型 (RRM)：加权几何平均 (WGA)、有序加权几何平均 (OWGA)、TOPSIS、VIKOR、PROMETHEE 和 ELECRE。特别是，我们可以构建几个 0-1 数学规划模型来计算选定的六种 MADM 方法在不完全属性权重信息下的备选方案的排名范围。然后，使用关于项目投资和世界大学学术排名 (ARWU) 的两个案例研究来证明在选定的六种 MADM 方法中，在不完整的属性权重信息下 RRM 的有效性。