Solar radiation prediction is an important process in ensuring optimal exploitation of solar energy power. Numerous models have been applied to this problem, such as numerical weather prediction models and artificial intelligence models. However, well-designed hybridization approaches that combine numerical models with artificial intelligence models to yield a more powerful model can provide a significant improvement in prediction accuracy. In this paper, novel hybrid machine learning approaches that exploit auxiliary numerical data are proposed. The proposed hybrid methods invoke different machine learning paradigms, including feature selection, classification, and regression. Additionally, numerical weather prediction (NWP) models are used in the proposed hybrid models. Feature selection is used for feature space dimension reduction to reduce the large number of recorded parameters that affect estimation and prediction processes. The rough set theory is applied for attribute reduction and the dependency degree is used as a fitness function. The effect of the attribute reduction process is investigated using thirty different classification and prediction models in addition to the proposed hybrid model. Then, different machine learning models are constructed based on classification and regression techniques to predict solar radiation. Moreover, other hybrid prediction models are formulated to use the output of the numerical model of Weather Research and Forecasting (WRF) as learning elements in order to improve the prediction accuracy. The proposed methodologies are evaluated using a data set that is collected from different regions in Saudi Arabia. The feature-reduction has achieved higher classification rates up to 8.5% for the best classifiers and up to 15% for other classifiers, for the different data collection regions. Additionally, in the regression, it achieved improvements of average root mean square error up to $5.6\%$ and in mean absolute error values up to 8.3%. The hybrid models could reduce the root mean square errors by 70.2% and 4.3% than the numerical and machine learning models, respectively, when these models are applied to some dataset. For some reduced feature data, the hybrid models could reduce the root mean square errors by 47.3% and 14.4% than the numerical and machine learning models, respectively.