Over the past 25 years, the evolution of the internet and the advances of wireless technologies have made a tremendous impact on lifestyle of people around the world. Together, these two factors have changed the way people communicate, work, and get their entertainment.In order to be always best connected for various applications, the network selection procedure in heterogeneous multi-access environment during vertical handover decision is intended to choose the most suitable network for mobile user. In this paper, a performance study using the fuzzy logic concept is done and the integration of UMTS and WiMAX network is taken as an example to show that the proposed vertical handoff decision algorithm is able to determine when a handoff is required, and selects the best access network that is optimized to network conditions, quality of service requirements, received signal strength, bandwidth requirements and user preferences.