Topological matrices for topological relations between fuzzy regions

Abstract

Topological relations are one of the most important aspects in GIS modeling. The topological relations between crisp spatial objects have been well identified. However, the topological relations between fuzzy spatial objects need more investigation. This paper discusses different definitions in fuzzy boundary and their differences and relations. One of the definitions is then selected as the fuzzy boundary for GIS. In order to identify the topological relations between fuzzy spatial objects, three intersection matrices, namely 3*3-intersection matrix, 4*4-intersection matrix and 5*5-intersection matrix, are proposed and formalized in a fuzzy topological space. These matrices are all applicable for identification of topological relations between fuzzy spatial objects. 152 topological relations between two simple fuzzy regions are identified based on the 4×4-intersection approach in R 2 .