Probabilistic representation and approximate inference of type-2 fuzzy events in Bayesian networks with interval probability parameters

It is necessary and challenging to represent the probabilities of fuzzy events and make inferences between them based on a Bayesian network. Motivated by such real applications, in this paper, we first define the interval probabilities of type-2 fuzzy events. Then, we define weak interval conditional probabilities and the corresponding probabilistic description. The expanded multiplication rule supporting interval probability reasoning. Accordingly, we propose the approach for learning the interval conditional probability parameters of a Bayesian network and the algorithm for its approximate inference. Experimental results show the feasibility of our method.