Some Topological Invariants and a Qualitative Topological Relation Model between Fuzzy Regions

Abstract

Topological relations are one of the most fundamental properties of spatial objects. The topological relations between crisp spatial objects have been well identified. However how to formalize the topological relations between fuzzy regions needs more investigation. The paper provides a theoretic framework for modeling topological relations between fuzzy regions. A novel topological model is formalized based on fuzzy topological space (FTS). In order to derive disjoint topological parts of a fuzzy set in FTS, the closure of a fuzzy set is decomposed into two novel parts, the core and the fringe. By use of the core, fringe and the outer of a fuzzy set in the FTS, a new 9-intersection matrix is proposed as a qualitative model for identification of topological relations between two simple fuzzy regions. Since all analysis is totally derived from FTS, therefore its results are universally applicable for GIS modeling and applications.