So far, the rank reversal (RR) phenomenon has been heavily discussed in the multiple criteria analysis literature. In this work, instead of focusing on RR occurrences within PROMETHEE II, an analysis of the third alternative with respect to a given pair of alternatives is conducted. The aim is to provide a way to identify third alternatives able to cause RR between a specific pair. This opens the question of building alternatives causing RR occurrences. Such alternatives can then be used to assess the resistance a given ranking has to RR. In the end, two different approaches are used. The first considers the number of third alternatives to be added to generate RR for a given pair of alternatives. While, the second one, provides a new threshold for RR occurrences in PROMETHEE II.

中文翻译：

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第三种方案对PROMETHEE II排名影响分析

到目前为止，排名反转（RR）现象已在多标准分析文献中进行了大量讨论。在这项工作中，我们没有关注 PROMETHEE II 中 RR 的发生，而是针对给定的一对替代方案对第三种替代方案进行了分析。目的是提供一种方法来识别能够在特定对之间引起 RR 的第三种替代方案。这就提出了建立导致 RR 发生的替代方案的问题。然后可以使用此类替代方案来评估给定排名对 RR 的抵抗力。最后，使用了两种不同的方法。第一个考虑要添加的第三个备选方案的数量，以便为给定的备选方案对生成 RR。而第二个则为 PROMETHEE II 中的 RR 发生提供了新的阈值。