Vague Spatial Data Types, Set Operations, and Predicates

Many geographical applications deal with spatial objects that cannot be adequately described by determinate, crisp concepts because of their intrinsically indeterminate and vague nature. Current geographical information systems and spatial database systems are unable to cope with this kind of data. To support such data and applications, we introduce vague spatial data types for vague points, vague lines, and vague regions. These data types cover and extend previous approaches and are part of a data model called VASA (Vague Spatial Algebra). Their formal framework is based on already existing, general exact models of crisp spatial data types, which simplifies the definition of the vague spatial model. In addition, we obtain executable specifications for the operations which can be immediately used as implementations. This paper gives a formal definition of the three vague spatial data types as well as some basic operations and predicates. A few example queries illustrate the embedding and expressiveness of these new data types in query languages.