In this paper, we describe various aspects of Explainable Artificial Intelligence (XAI) and we show that fuzzy systems can help to approach several of these aspects. We focus on the pioneering works of L. A. Zadeh that offer precious tools for the current XAI challenges. We show that they are not limited to approaches of natural language, but they also help to assist the user in understanding the meaning of the decisions made by artificial intelligence-based systems and to provide explanations about the way these decisions are made.