In this paper we propose a new multiple criteria decision aiding method to deal with sorting problems in which alternatives are evaluated on criteria structured in a hierarchical way and presenting interactions. The underlying preference model of the proposed method is the Choquet integral, while the hierarchical structure of the criteria is taken into account by applying the Multiple Criteria Hierarchy Process. Considering the Choquet integral based on a 2-additive capacity, the paper presents a procedure to find all the minimal sets of pairs of interacting criteria representing the preference information provided by the Decision Maker (DM). Robustness concerns are also taken into account by applying the Robust Ordinal Regression and the Stochastic Multicriteria Acceptability Analysis. Even if in different ways, both of them provide recommendations on the hierarchical sorting problem at hand by exploring the whole set of capacities compatible with the preferences provided by the DM avoiding to take into account only one of them. The applicability of the considered method to real world problems is demonstrated by means of an example regarding rating of European Countries by considering economic and financial data provided by Standard \& Poor's Global Inc.

中文翻译：

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具有分层结构的交互标准的稳健随机排序

在本文中，我们提出了一种新的多标准决策辅助方法来处理排序问题，其中根据以分层方式构建的标准并呈现交互来评估备选方案。所提出方法的基本偏好模型是 Choquet 积分，而标准的层次结构则通过应用多标准层次结构过程来考虑。考虑到基于 2-additive 容量的 Choquet 积分，该论文提出了一个程序来找到所有最小的交互标准对，代表决策者 (DM) 提供的偏好信息。通过应用稳健有序回归和随机多准则可接受性分析，还考虑了稳健性问题。即使以不同的方式，他们都通过探索与 DM 提供的偏好兼容的整套能力来提供关于手头的分层排序问题的建议，避免只考虑其中一个。通过考虑标准普尔全球公司提供的经济和金融数据，通过一个关于欧洲国家评级的例子，证明了所考虑的方法对现实世界问题的适用性。