Topological relations between fuzzy regions in a fuzzy topological space

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 deals with building a special fuzzy topological space for fuzzy sets. Based on it, a formal definition of simple fuzzy region is given. A 4 × 4-intersection and furthermore a 5 × 5-intersection approach are proposed for the formalism of topological relations. Finally 152 topological relations between two simple fuzzy regions are identified based on the 4 × 4-intersection approach in R2.