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Solar photovoltaic (PV) power generation is one of the most important sources for renewable energy. However, PV power generation is entirely dependent on the amount of downward solar radiation reaching the solar cells. This is determined by uncertain and uncontrollable meteorological factors such as temperature, humidity, wind speed, and direction, as well as other factors such as topographical characteristics. Good solar radiation prediction models can increase energy output while decreasing the operation costs of PV power generation. For example, in some provinces in China, PV stations are required to upload short-term online power forecast information to power dispatching agencies. Numerous AI, statistical, and numerical weather prediction models have been used in many real-world renewable energy applications, with a focus on modeling accuracy. However, there is a need for explainable AI models that could be easily understood, analyzed, and augmented by the stakeholders. In this article, we present a compact, explainable, and lifelong learning metaheuristic-based interval type-2 fuzzy logic system for solar radiation modeling. The generated model will be composed of a small number of short IF-Then rules that have been optimized via simulated annealing to produce models with high prediction accuracy. These models are updated through a life-long learning approach to maximize their accuracy and maintain interpretability. In the process of lifelong learning, the proposed method transferred the model's knowledge to new geographical locations with minimal forgetting. The proposed method achieved good prediction accuracy and outperformed on new geographical locations other transparent and black-box models by 13.2% as well as maintaining excellent generalization ability. The resulting models have been evaluated and accepted by experts, and thanks to the generated transparency, the experts were able to augment the models with their expertise, which increased the models' accuracy.