The Probability of Dual Hesitant Fuzzy Event and Its Applications to Bayesian Network Inferences

  • Xiu Jiu YuanEmail author
  • Xue Jun Zhao
  • Jiang Li
  • Lin Huang
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1074)


The concepts of probabilities and conditional probabilities of dual hesitant fuzzy events have been introduced. The basic properties, the countable additive formula, the law of total probability, the Bayes formula and the continuity of probability of classical probability theory are generalized to that of the probabilities of dual hesitant fuzzy events in frequently used \( t \)-norm and \( s \)-norm. The correlation coefficient between two dual hesitant fuzzy sets has been defined in random environment. An example of the dual hesitant fuzzy Bayesian network inference is presented finally.


Dual hesitant fuzzy set Dual hesitant fuzzy event Probability Bayes formula Bayesian network 


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Xiu Jiu Yuan
    • 1
    Email author
  • Xue Jun Zhao
    • 1
  • Jiang Li
    • 1
  • Lin Huang
    • 1
  1. 1.Department of Basic SciencesAir Force Engineering UniversityXi’anChina

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