A fuzzy topology for computing the interior, boundary, and exterior of spatial objects quantitatively in GIS

There have been many research developments on the conceptual description of topological relations between spatial objects. In order to practically implement these conceptual topological relations in a computer environment, we need to calculate the values of the topological relations. One of the theoretical bases for doing this is a computational fuzzy topology, which is the research focus of this study. Here, we present a development of computational fuzzy topology, which is based on the interior operator and closure operator. These operators are further defined as a coherent fuzzy topology-the complement of the open set is the closed set and vice versa; where the open set and closed set are defined by interior and closure operators-two level cuts. The elementary components of fuzzy topology for spatial objects-interior, boundary and exterior-are thus computed based on the computational fuzzy topology. An example of calculating the interior, boundary, and exterior of Mikania micrantha based on the aerial photographs of the Hong Kong countryside is provided in order to demonstrate the application of the theoretical development. Practically, the developed computational fuzzy topology is applicable for computing the values of fuzzy topological relations, such as defined conceptually by the 9-intersection model.