Comparative Analysis on the Effect of Triangular and Gaussian Membership Functions on Fuzzy Controlled Vehicle Platoon

  • Ajayi Ore-Ofe Ahmadu Bello University, Zaria
  • Nafisa S. Usman
  • Abdullahi Abubakar
  • Aminu Y. Zubairu
  • Risikat F. Adebiyi
  • Abdulfatai D. Adekale
  • Umar Abubakar
Keywords: Fuzzy, platoon, triangular, Gaussian, membership function


Fuzzy controlled vehicle platoon system provides a simplified yet robust approach to achieving platoon string stability and uniform inter-vehicular gap keeping in autonomous vehicle platoon. Most truck platoon is affected by delay of platoons which causes trucks not to maintain a constant inter-vehicular gap and speed, unknown uncertainties which may result in crash or accident. However, the fuzzification and defuzzification method adopted affects the final platoon characteristics of the platoon to a large extent, while also determining velocity stability timing, although researcher select a fuzzification/defuzzification method based on comfort, familiarity or simplicity. This paper proposes to compare the effect of fuzzification and defuzzification method on vehicle platoon, to provide evidence on the selection criteria and how it affects the controlled system. Simulation was done in MATLAB environment, and the fuzzy control approach was applied to a 3-vehicle autonomous platoon, which was a combination of triangular/centroid, triangular/bisector, triangular/mean with Gaussian/centroid, Gaussian/bisector and Gaussian/mean of maxima under the same platoon scenario. It was found that the best performing combination is the triangular/centroid with 4.44 secs velocity stability for vehicle V3, and 1.91 secs distance stability for follower vehicle, when compared to Gaussian/MoM with 79.88 secs velocity stability V3, and 85.89 secs for follower vehicle which is the worst performing combination.


Abdulnabi, A. (2017). PID Controller Design for Cruise Control System using Particle Swarm Optimization. Iraqi Journal for Computers Informatics (IJCI), 43(2), 30-35.

Abou-Zeid, H., Pervez, F., Adinoyi, A., Aljlayl, M., & Yanikomeroglu, H. (2019). Cellular V2X Transmission for Connected and Autonomous Vehicles Standardization, Applications, and Enabling Technologies. IEEE Consumer Electronics Magazine, 8(6), 91-98.

Ajayi, O.-o., Yahaya, S., & Umar, A. (2022). Application of Fuzzy Control System to Autonomous Vehicle Platoon. Nigerian Journal of Engineering, 29(2), 66-66.

Ajayi, O., Adebiyi, R., Abubakar, Z., Yusuf, S., Adekale, A., Abdulwahab, I., . . . Abdullahi, M. (2023). Simulation of Truck Platoon System using Anylogic Software. FUW Trends in Science & Technology Journal, 8(2), 224 – 227.

Axelsson, J. (2016). Safety in Vehicle Platooning: A Systematic Literature Review. IEEE Transactions on Intelligent Transportation Systems, 18(5), 1033-1045. doi:10.1109/TITS.2016.2598873

Chakraverty, S., Sahoo, D. M., & Mahato, N. R. (2019). Defuzzification. In Concepts of Soft Computing (pp. 117-127). Springer, Singapore: Springer.

Elliott, D., Keen, W., & Miao, L. (2019). Recent Advances in Connected and Automated Vehicles. Journal of Traffic and Transportation Engineering (English Edition), 6(2), 109-131. doi:

Fiengo, G., Lui, D. G., Petrillo, A., Santini, S., & Tufo, M. (2019). Distributed Robust PID Control for Leader Tracking in Uncertain Connected Ground Vehicles with V2V Communication Delay. IEEE/ASME Transactions on Mechatronics, 24(3), 1153-1165. doi:10.1109/TMECH.2019.2907053

Group, B. (2020). Technical Specifications BMW 520d Efficient Dynamics Edition. Available: htt[s://[.com/global/.

He, D., & Peng, B. (2020). Gaussian Learning-based Fuzzy Predictive Cruise Control for Improving Safety and Economy of Connected Vehicles. IET Intelligent Transport Systems, 14(5), 346-355.

Horowitz, R., & Varaiya, P. (2000). Control Design of an Automated Highway System. Proceedings of the IEEE, 88(7), 913-925. doi:10.1109/5.871301

Li, H., Tiwari, R., Pickert, V., & Dlay, S. (2018). Fuzzy Control for Platooning Systems Based on V2V Communication. Paper presented at the 2018 International Conference on Computing, Electronics & Communications Engineering (iCCECE), Southend, UK.

Li, S. E., Zheng, Y., Li, K., Wang, L.-Y., & Zhang, H. (2017). Platoon Control of Connected Vehicles from a Networked Control Perspective: Literature Review, Component Modeling, and Controller Synthesis. IEEE Transactions on Vehicular Technology, 1-1. doi:10.1109/TVT.2017.2723881

Ma, Y., Li, Z., Malekian, R., Zhang, R., Song, X., & Sotelo, M. A. (2018). Hierarchical Fuzzy Logic-based Variable Structure Control for Vehicles Platooning. IEEE Transactions on Intelligent Transportation Systems, 20(4), 1329-1340.

Nguyen, A.-T., Taniguchi, T., Eciolaza, L., Campos, V., Palhares, R., & Sugeno, M. (2019). Fuzzy Control Systems: Past, Present and Future. IEEE Computational Intelligence Magazine, 14(1), 56-68. doi:10.1109/MCI.2018.2881644

Nishida, M., & Sugeno, M. (1985). Fuzzy Control of Model Car. Fuzzy sets systems, 60(6), 103-113.

Nowakowski, C., Shladover, S. E., Lu, X.-Y., Thompson, D., & Kailas, A. (2015). Cooperative Adaptive Cruise Control (CACC) for Truck Platooning: Operational Concept Alternatives.

Pappis, C. P., & Mamdani, E. H. (1977). A Fuzzy Logic Controller for a Trafc Junction. IEEE Transactions on Systems, Man, and Cybernetics, 7(10), 707-717. doi:10.1109/TSMC.1977.4309605

Saade, J. J., & Diab, H. B. (2004). Defuzzification Methods and New Techniques for Fuzzy Controllers. Iranian Journal of Electrical and Computer Engineering (IJECE), 3(2), 161-174. doi:1682-0053(04)0238

Shrivastava, S. (2019). V2V Vehicle Safety Communication. In Connected Vehicles (pp. 117-155). Springer, Cham.: Springer.

Shukla, D., Kumar, V., & Prakash, A. (2020). Performance Evaluation of IEEE 802.11 p Physical Layer for Efficient Vehicular Communication. In Advances in VLSI, communication, and signal processing (pp. 51-60). Springer, Singapore: Springer.

Singh, H., & Lone, Y. A. (2020). Fuzzy Inference Systems. In Deep Neuro-Fuzzy Systems with Python (pp. 93-127): Springer.

Sugeno, M., Murofushi, T., Mori, T., Tatematsu, T., & Tanaka, J. (1989). Fuzzy Algorithmic Control of a Model Car by Oral Instructions. Fuzzy sets systems, 32(2), 207-219. doi:

Trabia, M., Shi, L. Z., & Hodge, N. E. (2006). A fuzzy logic controller for autonomous wheeled vehicles. In Jonas Buchli, Mobile Robots, Moving Intelligence, Advanced Robotic Systems International; pro literatur Verlag, 175-200.

Xavier, P., & Pan, Y.-J. (2009). A Practical PID-Based Scheme for the Collaborative Driving of Automated Vehicles. Paper presented at the Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, Shanghai, China.

Yen, J. (1999). Fuzzy logic: Intelligence, Control, and Information. Prentice Hall Upper Saddle River, NJ, : Pearson Education India.

Zadeh, L. A. (1965). Information and Control. Fuzzy sets, 8(3), 338-353.

Ziebinski, A., Cupek, R., Grzechca, D., & Chruszczyk, L. (2017). Review of advanced driver assistance systems (ADAS). Paper presented at the AIP Conference Proceedings.