An Enhanced Interactive and Multi-criteria Decision-Making (TODIM) Method with Probabilistic Dual Hesitant Fuzzy Sets for Risk Evaluation of Arctic Geopolitics

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.