Interactive analysis of time intervals in a two-dimensional space

Abstract

Time intervals are conventionally represented as linear segments in a onedimensional space. An alternative representation of time intervals is the Triangular Model (TM), which represents time intervals as points in a two-dimensional space. In this paper, the use of TM in visualising and analysing time intervals is investigated. Not only does this model offer a compact visualisation of the distribution of intervals, it also supports an innovative temporal query mechanism that relies on geometries in the two-dimensional space. This query mechanism has the potential to simplify queries that are hard to specify using traditional linear temporal query devices. Moreover, a software prototype that implements TM in a geographical information system (GIS) is introduced. This prototype has been applied in a real scenario to analyse time intervals that were detected by a Bluetooth tracking system. This application shows that TM has potential of supporting a traditional GIS to analyse interval-based geographical data.

Representing time intervals in a two-dimensional space: An empirical study

“…Note that can be different values for specific purposes. In this paper, we set  = 45°, to be consistent with earlier work Qiang, et al, 2010;Van de Weghe, et al, 2007). Considering this setting, the eight directions in the 2D space correspond to eight changing directions of interval properties ( Figure 6).…”

“…The potential and advantages of the TM in view of the analysis of time intervals has been elaborated in previous literatures (Qiang, et al, 2010;2012a;2012b). Following the TM, every interval is represented by a point at a specific location.…”

“…He argues that this approach is advantageous in various applications and theoretical and has comprehensively elaborated its use in qualitative interval reasoning and interval arithmetic. Van de Weghe et al (2007) (Qiang, et al, 2010) and interval analysis (Qiang, et al, 2012a;2012b, 2013. Since the TM displays a set of intervals within a stable point structure, it offers special insights into interval distributions, particularly when a large amount of intervals are represented in it.…”

“…The practical use of the TM has been demonstrated in Qiang et. al (2012a;2012b), where the TM is implemented in a GIS to support spatio-temporal analysis of interval-based geographic data. In these two papers, the TM has been applied to analyse the interval data generated from a Bluetooth tracking system and imperfect interval data in an archaeological database.…”

Bipolar Fuzzy Querying of Temporal Databases

“…Some proposals work with rough sets [19], other proposals rely on possibility distributions for representing uncertainty in time [11], [10]. In order to compare temporal possibility distributions, extensions of the classical Allen's operators [1] are defined in [18] and [16].…”