Modeling topological relations between fuzzy spatiotemporal regions over time

Abstract

Representing and identifying the topological relations between fuzzy spatiotemporal regions over time have an important significance in reasoning fuzzy spatiotemporal relations. The research issue of topological relations between fuzzy regions over time has attracted a lot of attention in the recent years. However, modeling topological relations needs to be further developed and it is still an open issue. In this paper, we extend the 9-Intersection model to establish a model for identification of topological relations between fuzzy spatiotemporal regions over time, and use extended intersection matrix to identify all possible topological relations. On the basis of our topological relation model, we extend two-dimensional Egg/Yolk model to three-dimensional space and calculate the corresponding intersection matrixes of each topological relations. Furthermore, after investigation of topological complexity and topological distance based on our proposed topological relation model, we propose a comprehensive conceptual neighborhood graph of the topological relations implemented on MATLAB.

Modeling Topological Relationships between Fuzzy Spatio-Temporal Objects

“…Spatio-temporal topological relationship is one of the most important and fundamental elements in spatio-temporal applications [20]. It plays an important role in the modeling of spatio-temporal knowledge.…”

“…In order to deal with the fuzziness and imprecision of spatio-temporal objects, several efforts have been made to model fuzzy spatio-temporal objects and their topological relationships, such as fuzzy set theory-based methods [15], [16], rough set theory-based method [17], point-set topology [13], motion-based approaches [14], [18], [19], and dimensional-extended method [20], [21].…”

“…In reality, however, the described methods do not represent continuous change of these relationships. In [20], by extending the two-dimensional Egg/Yolk model into three-dimensional space, the authors obtain 92 spatio-temporal topological relations between fuzzy spatio-temporal regions over time. For each relation, the authors give graphical representation and the corresponding intersection matrix.…”

“…However, the authors do not present the evolution of topological relations over time. In addition, the spatio-temporal relations in [17], [19], [20] are only defined in fuzzy regions, and not in fuzzy points and fuzzy lines. It should be noted that, although there have been some proposals for modeling topological relationships between fuzzy spatio-temporal objects, relatively little work has been done on integrating these topological relationships into databases to achieve fuzzy spatio-temporal queries.…”

“…Temporal changes of fuzzy line and fuzzy region are missing. At the same time, in order to model fuzzy topological relationships between fuzzy spatio-temporal objects, some efficient approaches have been proposed, mainly including fuzzy set theory-based methods [15], [16], rough set theory-based method [17], point-set topology [13], motion-based approaches [14], [18], [19], and dimensional-extended method [20], [21]. For example, in [17], the authors propose a method to model spatio-temporal topological relationships based on rough set theory.…”