The Decision Making Method Under the Probabilistic and Cognitive Environment

  • Zhinan HaoEmail author
  • Zeshui Xu
  • Hua Zhao
Part of the Uncertainty and Operations Research book series (UOR)


The concurrence of randomness and imprecision widely exists in real-world problems. Previous chapters study the decision-making methods under the epistemic uncertainty environment. How to solve the decision making problems involving both the aleatory and epistemic uncertainty? This chapter proposes the concept of the probabilistic dual hesitant fuzzy set to describe these two types of uncertainty in a single framework. The corresponding characteristics of this new extension of the fuzzy set are studied in detail. The visualization method based on the entropy is proposed to analyze the aggregated information and improve the final evaluation results. A case study of the Arctic geopolitical risk evaluation is presented to illustrate the validity and effectiveness of the proposed methods in this chapter.


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Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Command and Control Engineering CollegeArmy Engineering University of PLANanjingChina
  2. 2.Business SchoolSichuan UniversityChengduChina
  3. 3.Department of General EducationArmy Engineering University of PLANanjingChina

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