One of the most challenging topics for next-generation wireless networks is the process of vertical handoff since many of wireless technologies overlap each other and build a heterogeneous topology. Several parameters, pertaining to user/application requirements and network conditions, such as data rate, service cost, network latency, speed of mobile, and etc. must be considered in the handoff process of heterogeneous networks along with RSSI information. In this paper, adaptive fuzzy logic-based vertical handoff decision-making algorithms are presented for wireless overlay networks which consist of GSM/GPRS/Wi-Fi/IJMTS/WiMAX technologies. The parameters data rate, monetary cost, speed of mobile and RSSI information are processed as inputs of the proposed fuzzy-based systems. According to these parameters, an output value, which varies between 1 and 10, is produced. This output value is utilized to determine whether a handoff process is necessary or not and to select the best candidate access point in the vicinity. The results show that, compared to the traditional RSSI-based algorithm significantly enhanced outcomes can be achieved for both user and network as a consequence of the proposed fuzzy-based handoff systems. The simulation results are also compared with those of classical MADM (Multiple Attribute Decision Making) method, i.e. SAW (Simple Additive Weighting). According to the results obtained, the proposed vertical handoff decision algorithms are able to determine whether a handoff is necessary or not, properly, and select the best candidate access network considering the aforementioned parameters. Moreover, fuzzy-based algorithm noticeably reduces the number of handoffs compared to SAW-based algorithm. (C) 2012 Elsevier B.V. All rights reserved.