Objects with Broad Boundaries

Objects with broad boundaries are spatial objects, whose crisp boundaries are replaced by an area expressing the boundary’s uncertainty. There are two main interpretations for broad boundaries: (1) for positional uncertainty, the broad boundary represents the set of all possible positions among which the unknown boundary position is hidden; (2) for “fuzzy” boundaries, that is, boundaries that are by nature not crisp, the broad boundary represents their minimum and maximum extent. The main motivation for objects with broad boundaries is to record information about uncertainty together with the data. In this way, they represent a new geometric model that overcomes the limits of current spatial database models, which are a collection of lines (points, polylines and polygons). The geometric model of objects with broad boundaries takes into account a 3-valued indeterminacy of location (false, maybe, true), where “false” means that the point is not in the location, “true” means that the point is in the location and “maybe” means either that the point is with some probability in the location or that the point belongs, up to a certain membership value, to the location. Regions, lines and points with broad boundaries can be distinguished. In the case of lines, the broad interior can also be defined: a line with a broad boundary and broad interior is called an uncertain line.