Over View Properties and Application of Fuzzy Topology

Exploring the Use of Fuzzy Topology in Geographic Information Systems

Abstract

Currently most GISs represent natural phenomena by crisp spatial objects. In fact many natural phenomena have fuzzy characteristics. The representation of these objects in the crisp form greatly simplifies the processing of spatial data. However, this simplification cannot describe these natural phenomena precisely, and it will lead to loss of information in these objects. In order to describe natural phenomena more precisely, the fuzziness in these natural phenomena should be considered and represented in a GIS. This will allow the derivation of better results and a better understanding of the real world to be achieved. The central topic of this thesis focuses on the accommodation of fuzzy spatial objects in a GIS. Several issues are discussed theoretically and practically, including the definition of fuzzy spatial objects, the topological relations between them, the modeling of fuzzy spatial objects, the generation of fuzzy spatial objects and the utilization of fuzzy spatial objects for land cover changes. A formal definition of crisp spatial objects has been derived based on the highly abstract mathematics such as set theory and topology.