Abstract: The traditional classification models are always two­way decision models，which are based on the attributes or features of objects to accept or reject objects.However，in many cases，because of the inaccurate information，a number of objects belonging to different classes have the similar probability value.Therefore，classical two­way decisions based classifiers usually have a high probability to misclassify the vague objects.To obtain a lower misclassification rate，three­way decisions based classifiers adopt the deferment decision to deal with those vague objects.Those vague objects are classified into boundary region waiting for further processing.In order to facilitate the calculation，most three­way decision classifications are based on the single evaluation function.In single function based three­way decisions，all objects will be classified into the corresponding regions by comparing their conditional probabilities with the decision thresholds.The decision thresholds can be computed by three­way decision­theoretic rough set model，while the conditional probability of an object has to be provided by a specific classifier.In the computational efficiency，Naive Bayesian Rough set model combines the Naive Bayes and the three­way decision，resulting high computational efficiency.However，Naive Bayesian model is based on the assumption of conditional independence so that the obtained values are usually inaccurate.In view of the problems existing in the Naive Bayesian Rough set model，this paper proposes a three­way decisions based Bayesian network classifier，which introduces the Bayesian network model and combines the computation of the object’s conditional probability and decision thresholds together.Experimental results show that our proposed classifier can have a high accuracy.