The psychological factors of experts play a special role in the process of decision-making, especially in some situations that experts are not completely rational. Traditional decision-making methods always just focus on the aggregation of positive preference information, which do not take the negative attribute information into account at the same time. The probabilistic dual hesitant fuzzy set (PDHFS) is one of the latest fuzzy sets, which can depict experts’ positive and negative preference information with the corresponding probability at the same time. Therefore, to manage the applications with incomplete rationality and two opposite kinds of uncertain preference information, this paper considers the influence of psychological behavior on decision-making results and introduces an interactive method based on the prospect theory. Taking the advantages of PDHFSs in group decision-making problems, we propose the distance measure of PDHFSs, based on which an improved TODIM (TOmada deDecisão Iterativa Multicritério) method under the probabilistic dual hesitant fuzzy environment is also developed. Meanwhile, we provide the specific implementation process of the proposed method. The proposed improved TODIM is applied to the risk evaluation of Arctic geopolitics. We also make a comparison with the traditional aggregation method of PDHFSs. The difference among alternatives obtained by the proposed TODIM method with prospect theory is much greater than the traditional aggregation methods without prospect theory. This paper highlights the benefits and advantages of the proposed TODIM method that is developed based on the prospect theory and probabilistic dual hesitant fuzzy distance measure.

专家的心理因素在决策过程中发挥着特殊的作用，尤其是在专家不完全理性的情况下。传统的决策方法往往只关注正向偏好信息的聚合，而没有同时考虑负向属性信息。概率对偶犹豫模糊集（PDHFS）是最新的模糊集之一，它可以同时用相应的概率来刻画专家的正向和负向偏好信息。因此，针对不完全理性和两种相反的不确定偏好信息的应用程序的管理，本文考虑心理行为对决策结果的影响，引入基于前景理论的交互方法。利用PDHFS在群体决策问题中的优势，提出了PDHFS的距离测度，并在此基础上提出了概率双犹豫模糊环境下改进的TODIM（TOmada deDecisão Iterativa Multicritério）方法。同时给出了该方法的具体实现过程。提出的改进TODIM应用于北极地缘政治风险评估。我们还与 PDHFS 的传统聚合方法进行了比较。所提出的结合前景理论的TODIM方法所得到的备选方案之间的差异远大于传统的不结合前景理论的聚合方法。本文重点介绍了基于前景理论和概率双犹豫模糊距离测度开发的 TODIM 方法的好处和优点。