Increased environmental awareness coupled with the rising cost of energy have sparked a keen interest in the deployment of energy-efficient communication technologies over the infrastructure of cellular networks. Base stations (BSs) are responsible for the largest portion of power consumption and energy usage in cellular networks. Thus, sleep/wake-up scheduling strategies for BSs can significantly improve energy-efficiency (EE) of cellular networks. In this paper, we propose a Fuzzy Q-Learning (FQL) based energy-efficient sleep/wake-up mechanism for BSs in a heterogeneous network (HetNet). The goal is to save energy, without compromising the offered Quality of Service (QoS), by switching off the redundant BSs according to the local traffic profile and depending on the required area coverage and cell EE. The introduction of sleep mode for BSs may lead to a large-scale coverage loss, unless a specific remedial solution is exploited at the same time. To this end, we also propose to use device-to-device (D2D) communications to extend network coverage to the service areas of the switched-off BSs. Simulation results validate that the proposed framework provides significant improvements in power consumption and the EE.