The devices of Internet of Things (IoT) will grow rapidly in the near future, and the power consumption and radio spectrum management will become the most critical issues in the IoT networks. Long Term Evolution (LTE) technology will become a promising technology used in IoT networks due to its flat architecture, all-IP network, and greater spectrum efficiency. The 3rd Generation Partnership Project (3GPP) specified the Discontinuous Reception (DRX) to reduce device's power consumption. However, the DRX may pose unexpected communication delay due to missing Physical Downlink Control Channel (PDCCH) information in sleep mode. Recent studies mainly focus on optimizing DRX parameters to manage the tradeoff between the energy consumption and communication latency. In this paper, we proposed a fuzzy-based power saving scheduling scheme for IoT over the LTE/LTE-Advanced networks to deal with the issues of the radio resource management and power consumption from the scheduling and resource allocation perspective. The proposed scheme considers not only individual IoT device's real-time requirement but also the overall network performance. The simulation results show that our proposed scheme can meet the requirements of the DRX cycle and scheduling latency and can save about half of energy consumption for IoT devices compared to conventional approaches.