The wireless technologies in a heterogeneous wireless network usually differ in terms of, but not limited to, their offered bandwidths, operating frequencies and costs, coverage areas, and latencies. Currently, no single wireless technology claims to provide cost-effective services, which offers high bandwidths and low latencies to all mobile users in a large coverage area. This is where the need for well-organized vertical handoffs (VHOs) between heterogeneous wireless technologies become evident. This paper presents a new VHO algorithm which takes into account a complete set of system attributes to fulfill two tasks. The first task is to perform the VHO Necessity Estimation (VHONE) utilizing several parallel Fuzzy Logic Controllers (FLCs) with reduced rule sets to estimate the VHO necessity. The second task is the selection of the best network as the target for VHO, where a ranking algorithm is developed based on TOPSIS. Priority Weights for the different system attributes are calculated based on a Fuzzy Analytical Hierarchy Process (FAHP). Later, simulations based on four traffic classes (conversational, streaming, background, and interactive) in the presence of three wireless networks (WLAN, WMAN, and WWAN), are carried out using a comprehensive wireless simulation test-bed that contains all the necessary Radio Resource Management (RRM) modules.