Vehicular ad hoc network is considered a promising solution in Intelligent Transport System (ITS) and smart cities (SC) to enhance road safety, traffic efficiency, driver and passenger’s comfort. Much research has been conducted in this field to provide a reliable and efficient multi-hop broadcast protocol. The main problem that will be addressed in this paper is the deficiency of the existing VANET broadcasting protocols that leads to broadcast storm and message collisions. An inefficient VANET broadcasting protocol will also result in unreliable transmission, end-to-end delay. In this paper, a fuzzy logic inference assisted protocol is proposed to choose next hop relay vehicle to make sure that the broadcast messages will be received by all vehicles that might be affected with a minimum number of broadcasting. In the proposed fuzzy logic inference, distance, mobility and Received Signal Strength Indication (RSSI) are considered to select next forwarder relay. Network simulators have been developed to evaluate the performance of the proposed protocol and compare it with other protocols.