Modeling fuzzy topological predicates for fuzzy regions

Abstract

Spatial database systems and Geographical Information Systems (GIS) are currently only able to handle crisp spatial objects, i.e., objects whose extent, shape, and boundary are precisely determined. However, GIS applications are also interested in managing vague or fuzzy spatial objects. Spatial fuzziness captures the inherent property of many spatial objects in reality that do not have sharp boundaries and interiors or whose boundaries and interiors cannot be precisely determined. While topological relationships have been broadly explored for crisp spatial objects, this is not the case for fuzzy spatial objects. In this paper, we propose a novel model to formally define fuzzy topological predicates for simple and complex fuzzy regions. The model encompasses six fuzzy predicates (overlap, disjoint, inside, contains, equal and meet), wherein here we focus on the fuzzy overlap and the fuzzy disjoint predicates only. For their computation we consider two low-level measures, the degree of membership and the degree of coverage, and map them to high-level fuzzy modifiers and linguistic values respectively that are deployed in spatial queries by end-users.