A conceptual model of fuzzy topological relationships for fuzzy regions

Nowadays Geographical Information Systems (GIS) and spatial database systems are mainly able to handle crisp spatial objects, i.e., objects in space whose locations, extents, shapes, and boundaries are precisely determined. However, geoscientists and advanced GIS applications are increasingly interested in handling spatial objects that are characterized by the feature of spatial fuzziness and do not have sharp but blurred boundaries and/or interiors; hence, we call them fuzzy spatial objects. Examples are air polluted areas and temperature zones. In the same way as fuzzy spatial objects are blurred, the topological relationships (e.g., overlap, inside) between them are blurred too. In this conceptual paper, we propose a novel model to formally define fuzzy topological relationships for simple and complex fuzzy regions. Such a fuzzy relationship computes a membership degree between 0 and 1 that indicates to which extent this relationship holds. It is mapped to a high-level fuzzy modifier and transformed into a Boolean predicate that can be embedded into spatial queries.