The ship safety domain plays a significant role in collision risk assessment. However, few studies take the practical considerations of implementing this method in the vicinity of bridge-waters into account. Therefore, historical automatic identification system data is utilised to construct and analyse ship domains considering ship–ship and ship–bridge collisions. A method for determining the closest boundary is proposed, and the boundary of the ship domain is fitted by the least squares method. The ship domains near bridge-waters are constructed as ellipse models, the characteristics of which are discussed. Novel fuzzy quaternion ship domain models are established respectively for inland ships and bridge piers, which would assist in the construction of a risk quantification model and the calculation of a grid ship collision index. A case study is carried out on the multi-bridge waterway of the Yangtze River in Wuhan, China. The results show that the size of the ship domain is highly correlated with the ship's speed and length, and analysis of collision risk can reflect the real situation near bridge-waters, which is helpful to demonstrate the application of the ship domain in quantifying the collision risk and to characterise the collision risk distribution near bridge-waters.