High data rates in long-term evolution (LTE) networks can affect the mobility of networks and their performance. The speed and motion of user equipment (UE) can compromise seamless connectivity. However, a proper handover (HO) decision can maintain quality of service (QoS) and increase system throughput. While this may lead to an increase in complexity and operational costs, self-optimization can enhance network performance by improving resource utilization and user experience and by reducing operational and capital expenditure. In this study, we propose the self-optimization of HO parameters based on fuzzy logic control (FLC) and multiple preparation (MP), which we name FuzAMP. Fuzzy logic control can be used to control self-optimized HO parameters, such as the HO margin and time-to-trigger (TTT) based on multiple criteria, viz HO ping pong (HOPP), HO failure (HOF) and UE speeds. A MP approach is adopted to overcome the hard HO (HHO) drawbacks, such as the large delay and unreliable procedures caused by the break-before-make process. The results of this study show that the proposed method significantly reduces HOF, HOPP, and packet loss ratio (PLR) at various UE speeds compared to the HHO and the enhanced weighted performance HO parameter optimization (EWPHPO) algorithms.