Rough Sets in Approximate Spatial Reasoning

In spatial reasoning the qualitative description of relations between spatial regions is of practical importance and has been widely studied. Examples of such relations are that two regions may meet only at their boundaries or that one region is a proper part of another. This paper shows how systems of relations between regions can be extended from precisely known regions to approximate ones. One way of approximating regions with respect to a partition of the plane is that provided by rough set theory for approximating subsets of a set. Relations between regions approximated in this way can be described by an extension of the RCC5 system of relations for precise regions. Two techniques for extending RCC5 are presented, and the equivalence between them is proved. A more elaborate approximation technique for regions (boundary sensitive approximation) takes account of some of the topological structure of regions. Using this technique, an extension to the RCC8 system of spatial relations is presented.