Probabilistic Fuzzy Bayesian Network

Most real world problems involve some kind of uncertainty, like randomness, vagueness or ignorance. In the computational intelligence area there are a number of techniques capable of dealing with each kind of uncertainty. However, it is possible that a problem involves more than one kind of uncertainty at the same time, and in this case, hybrid solutions must be sought. Bayesian networks are probabilistic graphical models capable of modeling statistical uncertainty and are widely applied in many practical problems. Despite Bayesian networks being able to deal with randomness, they are unable to model linguistic vagueness. 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 classical fuzzy systems are unable to model statistical uncertainty, Probabilistic Fuzzy Systems were developed in order to account for both kind of uncertainties. In this work we propose the Probabilistic Fuzzy Bayesian Network as a combination of both probabilistic fuzzy systems and bayesian networks, also capable of simultaneously modeling both kinds of uncertainty using the concepts of bayesian inference and probabilistic fuzzy systems. 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. For validation of the proposed model, experiments are done using benchmark classification data sets from the UCI machine learning repository and the results are then compared with other machine learning techniques.