The Probability of Dual Hesitant Fuzzy Event and Its Applications to Bayesian Network Inferences
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.
KeywordsDual hesitant fuzzy set Dual hesitant fuzzy event Probability Bayes formula Bayesian network
- Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision. In: The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, pp. 1378–1382 (2009)Google Scholar
- Wang, L., Shen, Q.G., Zhu, L.: Dual hesitant fuzzy power aggregation operators based on Archimedean t-conorm and t-norm and their application to multiple attribute group decision making. Appl. Soft Comput. J. 38©, 23–50 (2016)Google Scholar
- Zhang, W.X., Wang, G.J., et al.: Introduction of Fuzzy Mathematics, 1st edn. Xi’an Jiao Tong University Press, Xi’an (2005). (in Chinese)Google Scholar