Video streaming over Vehicular Ad Hoc Networks is a promising technique (VANETs), and it has gained great importance in the last few years. The highly dynamic topology of VANETs makes high-quality video streaming very challenging. In order to provide the most useful camera views to the vehicles, clustering and cluster head selection techniques are used. Too frequent camera view changes can be annoying; therefore, we propose a new stable clustering algorithm to ensure a stable live road surveillance service without interruptions for vehicles that do not have enough vision area. In the proposed solution, we integrated Density-Based Spatial Clustering of Applications with Noise (DBSCAN) with Fuzzy Logic Control (FLC). DBSCAN is used to form the clusters, while FLC is used to find the best cluster head for the cluster. Different parameters are utilized like density parameters for DBSCAN, and relative speed, acceleration, leadership degree and vision area for fuzzy logic. Our proposed algorithm showed better results in terms of cluster lifetime and vehicle status change. Our proposed algorithm has been compared with another clustering scheme to prove the effectiveness of our proposed algorithm.