ROSA: An Algebra for Rough Spatial Objects in Databases

A fundamental data modeling problem in geographical information systems and spatial database systems refers to an appropriate treatment of the vagueness or indeterminacy features of spatial objects. Geographical applications often have to deal with spatial objects that cannot be adequately described by the determinate, crisp concepts exclusively available in these systems since these objects have an intrinsically indeterminate and vague nature. The goal of this paper is to show that rough set theory can be leveraged in an elegant manner to seamlessly model this kind of spatial data. Our approach introduces novel rough spatial data types for rough points, rough lines, and rough regions that can be employed as attribute types in database schemas. These data types are part of a data model called ROSA (ROugh Spatial Algebra). Their formal framework is based on already existing, general, exact models of crisp spatial data types, which simplifies the definition of the rough spatial model. In addition, we obtain executable specifications for the operations on rough spatial objects; these can be immediately used as implementations. This paper gives a formal definition of the three rough spatial data types as well as some basic operations.