In this paper, we introduce two independent hybrid mining algorithms to improve the classification accuracy rates of decision tree (DT) and naïve Bayes (NB) classifiers for the classification of multi-class problems. Both DT and NB classifiers are useful, efficient and commonly used for solving classification problems in data mining. Since the presence of noisy contradictory instances in the training set may cause the generated decision tree suffers from overfitting and its accuracy may decrease, in our first proposed hybrid DT algorithm, we employ a naïve Bayes (NB) classifier to remove the noisy troublesome instances from the training set before the DT induction. Moreover, it is extremely computationally expensive for a NB classifier to compute class conditional independence for a dataset with high dimensional attributes. Thus, in the second proposed hybrid NB classifier, we employ a DT induction to select a comparatively more important subset of attributes for the production of naïve assumption of class conditional independence. We tested the performances of the two proposed hybrid algorithms against those of the existing DT and NB classifiers respectively using the classification accuracy, precision, sensitivity-specificity analysis, and 10-fold cross validation on 10 real benchmark datasets from UCI (University of California, Irvine) machine learning repository. The experimental results indicate that the proposed methods have produced impressive results in the classification of real life challenging multi-class problems. They are also able to automatically extract the most valuable training datasets and identify the most effective attributes for the description of instances from noisy complex training databases with large dimensions of attributes.