Spatio-temporal topological relationships based on rough set

In order to model natural phenomena and their relationships properly, their fuzziness and vagueness must be considered. Rough set can handle the inherent fuzziness of object. Topological relations are among the most important definable characters between two indeterminate spatio-temporal objects. This paper proposes a new way for modeling and constructing topological relationships between spatio-temporal objects under the umbrella of rough topological relationships in space and time. Lower bound region, outer region and boundary region are considered as interior, exterior and boundary, respectively; both for region and time intervals. The intersection matrix of the relations is then derived and used to interpret the spatial relationships. Based on the lower and upper part of a time interval the temporal topological relations are defined. And finally the integration of spatial and temporal relations in temporal space is represented. As a case study, satellite images are selected, classified, vectorized, and the land cover changes are monitored. The intersection matrix is estimated and the advantages of the model are presented in detail. Results show that rough set theory models uncertainty of spatio-temporal objects in a transparent and explainable way.