Multi-dimensional classification is a generalization of supervised classification that considers more than one class variable to classify. In this paper we review the existing multi-dimensional Bayesian classifiers and introduce a new one: the KDB multi-dimensional classifier. Then we define different classification rules for multi-dimensional scope. Finally, we introduce a structural learning approach of a multi-dimensional Bayesian classifier based on the multi-objective evolutionary algorithm NSGA-II. The solution of the learning approach is a Pareto front representing different multi-dimensional classifiers and their accuracy values for the different classes, so a decision maker can easily choose the classifier which is more interesting for the particular problem and domain.