In the context of global warming, renewable energy sources, particularly wind and solar power, have garnered increasing attention in recent decades. Accurate forecasting of the energy output in microgrids (MGs) is essential for optimizing energy management, reducing maintenance costs, and prolonging the lifespan of energy storage systems. This study proposes an innovative approach to solar irradiance forecasting based on the theory of belief functions, introducing a novel and flexible evidential method for short-to-medium-term predictions. The proposed machine learning model is designed to effectively handle missing data and make optimal use of available information. By integrating multiple predictive models, each focusing on different meteorological factors, the approach enhances forecasting accuracy. The Yager combination method and pignistic transformation are utilized to aggregate the individual models. Applied to a publicly available dataset, the method achieved promising results, with an average root mean square error (RMS) of 27.83 W/m2 calculated from eight distinct forecast days. This performance surpasses the best reported results of 30.21 W/m2 from recent comparable studies for one-day-ahead solar irradiance forecasting. Comparisons with deep learning-based methods, such as long short-term memory (LSTM) networks and recurrent neural networks (RNNs), demonstrate that the proposed approach is competitive with state-of-the-art techniques, delivering reliable predictions with significantly less training data. The full potential and limitations of the proposed approach are also discussed.