3D Fuzzy Topological Relations Modeling in GIS Environment

Nowadays, geospatial information systems (GIS) are widely used to solve different spatial problems based on various types of fundamental data: spatial, temporal, attribute and topological relations. Topological relations are the most important part of GIS which distinguish it from the other kinds of information technologies. One of the important mechanisms for representing topological relations between spatial objects is spatial topology. These mechanisms help users to model spatial analysis on the objects simply and efficiently. Topological relations which used for the analysis are influenced by uncertain resources such as: inaccuracy and error of measurements, vagueness to describe information, incompleteness, inconsistency and impreciseness. Then, the fuzzy set theory as an ideal tool can help to handle these uncertain resources in the topological relations. Our methodology relies on the 3D fuzzy 9-intersection, which is a generalization of the crisp 9-intersection of Egenhofer and co-workers. The similarity between the 3D fuzzy and the crisp 9-intersection enables the decision variables, to be derived. The decision variable includes a semantic part and a quantifier. Since determination of the decision variable depends on the definition of the boundary of the fuzzy regions, we try to present a useful method for computing fuzzy boundaries. For this purpose each point of a Fuzzy region has partial membership degree to Interior, Boundary and Exterior set of a region. In order to derive the topological relations between fuzzy spatial objects, the 9-intersection approach is updated into the 3*3-intersection approach in the crisp fuzzy topological space. The topological relations between simple fuzzy regions can be identified based on the topological invariants in the intersections of the matrices. With respect to this, we try to check and complete our information about how we can define 3D fuzzy topological relations between spatial objects and propose an efficient method for simulating relationships and extracting decision variables. This subject is applied for the application of "determining risk areas of Kuwait oil well air pollutions plumes on the southwestern forest areas of Iran". For this purpose, decision variables are extracted based on 3D fuzzy topological relations between air pollution plumes and a forest area, then, reasoned using defined proper rules in the knowledge base part of a spatial reasoning system. When smoke plumes move toward a forest area: data extractor extracts the smokes fuzzy areas form remote sensing satellite images, and topological simulator computes the strength and type of topological relationships and sends the extracted information to a designed knowledge based system. The final results show 20% improvement in reasoning results by adding inclusion index and 3D topological rations to the knowledge part of designed system.