Probabilistic dual hesitant fuzzy set and its application in risk evaluation

The concurrence of randomness and imprecision widely exists in real-world problems. To describe the aleatory and epistemic uncertainty in a single framework and take more information into account, in this paper, we propose the concept of probabilistic dual hesitant fuzzy set (PDHFS) and define the basic operation laws of PDHFSs. For the purpose of applications, we also develop the basic aggregation operator for PDHFSs and give the general procedures for information fusion. Next, we propose a visualization method based on the entropy of PDHFSs so as to analyze the aggregated information and improve the final evaluation results. The proposed method is then applied to the risk evaluations. A case study of the Arctic geopolitical risk evaluation is presented to illustrate the validity and effectiveness. Finally, we discuss the advantages and the limitations of the PDHFS in detail.