VASA: An algebra for vague spatial data in databases

Many geographical applications deal with objects in space that cannot be adequately described by determinate, crisp spatial concepts because of their intrinsically indeterminate and vague nature. Geographical information systems and spatial database systems are currently unable to cope with this kind of data. To support the efficient representation, querying, and manipulation of vague spatial data in a database context, we present a formal data model called vague spatial algebra (VASA). This algebra comprises a set of vague spatial data types for vague points, vague lines, and vague regions together with a comprehensive collection of vague spatial operations and vague topological predicates. One of VASA's main benefits is that its formal framework is based on well known, general, and exact models of crisp spatial data types. This enables an exact definition of the vague spatial model since we can build upon an already existing theory of spatial data types. In particular, crisp spatial data types turn out to be a special case of their vague counterparts. In addition, our approach enables executable specifications for the operations, which can be immediately used as implementations. The article offers a precise and conceptually clean foundation for implementing a DBMS extension for vague spatial data and demonstrates the embedding of these new data types as attribute data types in a database schema as well as the incorporation of vague spatial operations and predicates into queries formulated in an SQL-like query language. All concepts have been verified in a prototype implementation.