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Vehicle-to-Everything communications (V2X) are becoming increasingly popular as a solution for safer roads and better traffic management. One of the essential protocols in V2X is the Dedicated Short Range Communication (DSRC) protocol suite. DSRC includes the IEEE 802.11p protocol that operates at the medium access control (MAC) and physical (PHY) layers. Upon collision, the IEEE 802.11p MAC layer applies a carrier sense multiple access/collision avoidance (CSMA/CA) mechanism that randomly selects a backoff time to re-check the channel activity and then retransmit. However, the random selection of the backoff time may lead to further packet collisions that decrease the utilization of the communication channel, which suffers from a limited bandwidth in the first place. This paper proposes a fuzzy model based on rational decision-making, which we call F-802.11p, to improve the IEEE 802.11p protocol backoff time selection by limiting the IEEE 802.11p beacon messages to better use of the available bandwidth. A simulation study presents the evaluation of our work compared to IEEE 802.11p. We deployed the simulation software in two scenarios: the Veins Framework map and the map of New Administrative Cairo in Egypt. We base our comparison on slots backoff, times into backoff, PHY busy time, MAC busy time, total lost packets, and generated/received beacon messages. Simulation results show that both protocols have comparable results in slots backoff, times into back off, and the generated beacon messages. At the same time, our F-802.11p significantly outperforms the IEEE 802.11p in PHY busy time, MAC busy time, total lost packets, and the received beacon messages in both scenarios.