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 events have probabilities and conditional probabilities, which can be used in Bayesian network inference.

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

Key Takeaway: Dual hesitant fuzzy events have probabilities and conditional probabilities, which can be used in Bayesian network inference.