Vertical handover management plays an essential role in wireless network technologies, mainly due to the rapid development of various radio access technologies (RATs) that require users to connect seamlessly from one RAT to another. However, in multiple RAT environments, vertical handover management encounters different challenges, including unnecessary handovers, handover failures, ping-pong handovers, and unsuitable access network selection. Essential in vertical handover management is maintaining the desired quality of service (QoS) by the mobile device user. The seamless movement of mobile device users as they run various applications depends on a well-performing vertical handover decision-making algorithm. This bears special significance in a heterogeneous network environment. This paper proposes a vertical handover algorithm that considers user preferences (i.e., a vertical handover algorithm that evaluates the application currently running on a user device). The main objective of the algorithm is to determine when it is necessary to perform the handover, depending on the applications running on the mobile device. The proposed algorithm utilizes a fuzzy logic system to assess whether the handover is necessary and a multiattribute decision-making (MADM) method to select the best available radio access network. A simulation scenario involving different applications at various mobile device velocities was developed. The results proved the algorithm’s effectiveness compared to some of the earlier proposed vertical handover algorithms. At velocities below 10 m/s and 30 m/s, the proposed algorithm had 0% and 15.02% unnecessary handovers, respectively, while the technique for order preference by similarity to ideal solution (TOPSIS) utility’s function-based algorithm obtained 12.38% and 23.24% at the same velocities, respectively. In addition, compared to TOPSIS, the obtained results of the proposed algorithm demonstrated a lower handover failure rate and ping-pong rate for a velocity span of 1–30 m/s for the considered user applications.