Problem statement: The Next generation wireless networks are heterogeneous in nature where different Radio Access Technologies (RAT) coexists in the same coverage area. The user terminal should be able to pick the best access technology such as Wireless Local Area Network (WLAN), Wireless Wide Area Networks (WWAN), the Universal Mobile Telecommunication Systems (UMTS) and the Global System for Mobile Telecommunication (GSM)/Enhanced Data rate for GSM Evolution (EDGE) Radio Access Network (GERAN) at its current location and use the access technology seamlessly for the provision of desired service. The goal is to select the most suitable Radio Access Technology (RAT) for each user. It is important that suitable decision making algorithm should be designed such that all the important characteristics of the system are taken into account when making the radio access selection. Approach: For this reason, this research work proposes a methodology to select the best access network among WLAN and WWAN under the input criteria Signal Strength of both networks, speed of the mobile terminal and network coverage of both networks and Quality of Service (QoS). Hence, in this work, a new hybrid multi objective decision making algorithm employing weighing function and particle swarm optimization is proposed for fuzzy based Radio Access Technology selection of Heterogeneous wireless networks. Results: The end results indicate that the proposed algorithm outperforms better than the existing methods. Conclusion: Inferences from the results indicate that by using the proposed algorithm, best RAT can be selected for the user with a minimal time constraint.