Modeling Topological Relationships between Fuzzy Spatio-Temporal Objects

Topological relationships between spatio-temporal objects are the most fundamental elements in spatio-temporal database systems, GIS, and image database systems. The research issue of modeling topological relationships has increasingly attracted attention, especially for querying of spatio-temporal objects and reasoning of topological relationships. Currently, topological relationship operating on spatio-temporal objects with precisely defined boundaries has been well studied. However, in the real world, spatio-temporal objects are not always crisp but with the nature of fuzziness and imprecision. Therefore, how to model topological relationship between fuzzy spatio-temporal objects is a significant topic and needs more investigations. This paper presents a study on modeling topological relationships between fuzzy spatio-temporal objects. Firstly, we give a model of fuzzy spatio-temporal objects in three-dimensional space and define those objects as moving fuzzy points, moving fuzzy lines, and moving fuzzy regions. On this basis, we propose a model for identifying basic topological relations between fuzzy spatio-temporal objects. Furthermore, in order to describe the evolution of basic topological relations over time, we give a model of complex topological relationships which are the sequences of basic relationships. The benefit of this model is that the complex topological relationships can be used as fuzzy spatio-temporal query operators in query languages. Finally, we provide some query examples to demonstrate fuzzy spatio-temporal queries in spatio-temporal database.