A geometric theory of vague boundaries based on supervaluation

Abstract

The representation of geographical objects with vague or fuzzy boundaries still poses a challenge to current geographical information systems. The paper presents a geometric account to deal with spatial vagueness. This approach is based on ideas of the theory of supervaluation. To capture vague spatial information current geographical information systems mainly employ fuzzy set theory and fuzzy logic. The proposed geometric theory is contrasted with fuzzy theories regarding the representation of vague spatial objects and the inferences that can be drawn about the objects. Opposed to fuzzy theories, the proposed theory does not rely on a numerical representation to model spatial vagueness, but is still compatible with it. Therefore, the approach is able to support spatial databases in qualitative spatial inferences.