Vehicle platooning is seen as an enabler to improve driving safety, traffic congestion and stress-free driving. A platoon is a highly non-linear system and fuzzy control is able to deal with those systems. This paper presents a pioneering solution to the complex problem of vehicle platooning. Our adaptive controller seamlessly integrates fuzzy logic with conventional PID control technology, thereby ensuring safe and efficient travel for vehicles within a platoon. The key objectives of this controller encompass the maintenance of a consistent inter-vehicle time gap and the consideration of time-varying parameter uncertainties and communication delays between vehicles. It provides mathematical proof of the stability of the platoon formation using the Routh-Hurwitz theorem and a set of equations that describe the platoon's overall performance. Simulation results show that the proposed controller is effective in controlling vehicle platoons, even in the presence of random communication delays, resulting in improved driving safety and reduced traffic congestion.