Computing the fuzzy topological relations of spatial objects based on induced fuzzy topology

Abstract

For modeling the topological relations between spatial objects, the concepts of a bound on the intersection of the boundary and interior, and the boundary and exterior are defined in this paper based on the newly developed computational fuzzy topology. Furthermore, the qualitative measures for the intersections are specified based on the α‐cut induced fuzzy topology, which are (Aα∧∂A)(x)<1−α and ((Ac)α∧∂A)(x)<1−α. In other words, the intersection of the interior and boundary or boundary and exterior are always bounded by 1−α, where α is a value of a level cutting. Specifically, the following areas are covered: (a) the homeomorphic invariants of the fuzzy topology; (b) a definition of the connectivity of the newly developed fuzzy topology; (c) a model of the fuzzy topological relations between simple fuzzy regions in GIS; and (d) the quantitative values of topological relations can be calculated.