The intermittent nature associated with photovoltaic (PV) generation is a challenging problem for the optimal planning and efficient management in smart grids. A reliable forecasting model of solar irradiance can play an essential role in allowing high PV penetrations without degrading the grid performance. For this purpose, most related works either use individual forecasting models or ensemble approaches (e.g., weighted average), ignoring the interaction between the values to be aggregated and thus may worsen the forecasting reliability. Differently, we propose a reliable solar irradiance forecasting method based on long short-term memory (LSTM) models and an aggregation function based on Choquet integral. This novel combination has the following features: 1) LSTM models can achieve accurate predictions because they model the temporal changes in solar irradiance, thanks to their recurrent architecture and memory units, and 2) the Choquet integral can model the interaction between the inputs to be aggregated through a fuzzy measure. This aggregation technique can determine the largest consistency among the conflicting forecasting results, taking advantage of each individual model. To demonstrate the effectiveness of the proposed approach, we compare it with several forecasting methods using six realistic datasets collected from different sites in Finland in which solar irradiance is intermittent. The comparison reveals the high reliability of the proposed forecasting model with different sites and solar profiles.