Nowadays, one of the most important challenges in heterogeneous networks is the connection consistency between the mobile station and the base stations. Furthermore, along the roaming process between the mobile station and the base station, the system performance degrades significantly due to the interferences from neighboring base stations, handovers to inaccurate base station and inappropriate technology selection. In this paper, several algorithms are proposed to improve mobile station performance and seamless mobility across the long-term evolution (LTE) and Worldwide Interoperability for Microwave Access (WiMAX) technologies, along with a minimum number of redundant handovers. Firstly, the enhanced global positioning system (GPS) and the novel received signal strength (RSS) prediction approaches are suggested to predict the target base station accurately. Then, the multiple criteria with two thresholds algorithm is proposed to prioritize the selection between LTE and WiMAX as the target technology. In addition, this study also covers the intercell and cochannel interference reduction by adjusting the frequency reuse ratio 3 (FRR3) to work with LTE and WiMAX. The obtained results demonstrate high next base station prediction efficiency and high accuracy for both horizontal and vertical handovers. Moreover, the received signal strength is kept at levels higher than the threshold, while maintaining low connection cost and delay within acceptable levels. In order to highlight the combination of the proposed algorithms' performance, it is compared with the existing RSS and multiple criteria handover decision algorithms.