Densely-deployed heterogeneous networks (HetNets) with large number of small cell base stations (SBSs) will constitute one of the main pillars of emerging 5G wireless systems. While such dense deployments of HetNets can help in achieving capacity requirements of 5G networks, they can also result in a significant increase in energy consumption. Since there may not be many associated users in certain SBSs, intelligently turning them off while not seriously degrading system throughput and handover performance can improve energy savings in HetNets. In this paper, we consider a fuzzy logic based game-theoretic framework for energy efficiency improvements in HetNets. We develop fuzzy decision rules for handovers and target base station selection while simultaneously considering the energy/spectral efficiency and handover performance. Our results show that energy consumption can be improved considerably especially for small number of active users and for high user velocities, while also managing ping-pong handovers and cell loads.