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With the increasing use of mobile GPS (global positioning system) devices, a large volume of trajectory data on users can be produced. In most existing work, trajectories are usually divided into a set of stops and moves. In trajectories, stops represent the most important and meaningful part of the trajectory; there are many data mining methods to extract these locations. DBSCAN (density-based spatial clustering of applications with noise) is a classical density-based algorithm used to find the high-density areas in space, and different derivative methods of this algorithm have been proposed to find the stops in trajectories. However, most of these methods required a manually-set threshold, such as the speed threshold, for each feature variable. In our research, we first defined our new concept of move ability. Second, by introducing the theory of data fields and by taking our new concept of move ability into consideration, we constructed a new, comprehensive, hybrid feature-based, density measurement method which considers temporal and spatial properties. Finally, an improved DBSCAN algorithm was proposed using our new density measurement method. In the Experimental Section, the effectiveness and efficiency of our method is validated against real datasets. When comparing our algorithm with the classical density-based clustering algorithms, our experimental results show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In the paper, we introduce a notion of a non-Archimedean metric space endowed with the non-Archimedean Pompeiu-Hausdorff metric. Using the direct and fixed point methods, we study the Hyers-Ulam stability of set-valued AQ-functional equations in the framework of complete non-Archimedean metric spaces. We indeed present an interdisciplinary relations between the theory of set-valued mappings, the theory of non-Archimedean spaces and the stability theory of functional equations. [ABSTRACT FROM AUTHOR]

The non-Archimedean normed space theory is an important research object in mathematical physics whose triangle inequality holds in a stronger form. In this note, we propose a generalized chordal distance and a non-Archimedean chordal distance for intuitionistic fuzzy sets. An illustrative example is given to calculate the constructed distances with the different parameters. And some experiments show that the new distances based on chordal distance and non-Archimedean distance are more efficient than the Euclidean-like distances in pattern recognition. [ABSTRACT FROM AUTHOR]