Bayesian networks are probabilistic graphical models capable of modeling statistical uncertainty and are widely applied in many classification problems. Specifically, Naive Bayesian networks are largely used due to their simple, naive structure, while still producing precise results. Fuzzy systems, on the other hand, are a well known technique capable of dealing with linguistic vagueness by representing knowledge with simple and interpretable rules and membership functions. As traditional fuzzy systems are unable to model statistical uncertainty, Probabilistic Fuzzy Systems were developed in order to account for both kinds of uncertainties. In this work we propose the Probabilistic Fuzzy Naive Bayes classifier as a combination of both probabilistic fuzzy systems and naive bayesian networks, also capable of simultaneously modeling both kinds of uncertainties. The proposed model is firstly applied in a very simple classification problem in order to show its potential and advantage over traditional naive bayes classifiers, while maintaining their interpretability. For validation, experiments were done using benchmark classification data sets from the UCI machine learning repository and the results are then compared with other similar alternate methods.