A framework for modeling uncertain relationships between spatial objects in GIS based on fuzzy topology

Boundaries of spatial objects in geographical information systems (GIS) may be vague or fuzzy and the classical set theory which is based on crisp boundary. Since the crisp set-based description may not match to what in the real world, and lead a wrong description in GIS and corresponding spatial analysis. As the fuzzy theory gives us another way of representing objects in GIS, we consider fuzzy sets and investigate corresponding fuzzy topological relations.; The objectives of the thesis as follows: (1) To solve the existing problems of 9-intersection model by introducing several useful intersection models to describe the relations of point to point, point to line, point to region, line to line, line to region and region to region respectively. (2) To the handle the vague or fuzzy models by investigating the topological relations in the cases of point to point, point to line, point to region, line to line, line to region and region to region respectively. (3) To develop models for quantitatively compute uncertainty topological relations between spatial objects in GIS. (4) To develop qualitative fuzzy topological relations under several invariant properties which including quasi-coincidence, connective and others. (5) To apply the developed fuzzy topology to image processing.; The main focus of this thesis is mainly on modeling topological relations between spatial objects in GIS. Several issues on modeling topological relations between spatial objects are addressed, which including (a) defining topological relations and fuzzy GIS elements; (b) proving that topological relations between spatial objects are shape dependent; (c) modeling topological relations between spatial objects by using the concepts of quasi-coincidence and quasi-difference in fuzzy topology theory; (d) creating the computable fuzzy topology for practically implementing these conceptual topological relations in a computer environment.; The first issue is giving a new definition of the topological relations between two spatial objects which actually is an extended model for topological relations between two spatial objects. For this issue, we have found out that the number of topological relations between the two sets is not as simple as finite; actually, it is infinite and can be approximated by a sequence of matrices. Moreover, as point, line and region (polygon) are the basic elements in GIS, thus we define them based on a fuzzy set.; Topology is normally considered as shape independent of spatial objects. This may not necessarily be true in describing relations between spatial objects in GIS. We present a proof that the topological relations between spatial objects are dependent on the shape of spatial objects. (Abstract shortened by UMI.)...