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Modelling imperfect time intervals in a two-dimensional space

机译：在二维空间中建模不完美的时间间隔

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Every event has an extent in time, which is usually described by crisp time intervals. However, under some circumstances, temporal extents of events are imperfect, and therefore cannot be adequately modelled by crisp time intervals. Rough sets and fuzzy sets are two frequently used tools for representing imperfect temporal information. In this paper, we apply a two-dimensional representation of crisp time intervals, which is called the Triangular Model ™, to investigate rough time intervals (RTIs) and fuzzy time intervals (FTIs). With this model, RTIs and FTIs, as well as their temporal relations, can be represented as graphics (I.e. discrete geometries or continuous fields) in a two-dimensional time space. Compared to the traditional linear representation of time intervals, we found that TM provides a more compact and clearer representation of imperfect time intervals and relations. Moreover, temporal queries of imperfect intervals can be graphically addressed in TM, which is closer to human intuition than mathematical expressions. As human minds are more efficient in perceiving and processing graphic representations than numerical representations, we believe TM can be applied as a valuable assistant tool for analysing and reasoning about imperfect time intervals.
机译：每个事件都有一个时间范围，通常用明确的时间间隔来描述。但是，在某些情况下，事件的时间范围是不完善的，因此无法通过清晰的时间间隔对其进行充分建模。粗糙集和模糊集是表示不完善的时间信息的两个常用工具。在本文中，我们使用清晰时间间隔的二维表示（称为Triangular Model™）来研究粗略时间间隔（RTIs）和模糊时间间隔（FTI）。利用该模型，RTI和FTI以及它们的时间关系可以表示为二维时间空间中的图形（即，离散几何或连续场）。与传统的时间间隔线性表示相比，我们发现TM提供了更完善，更清晰的不完美的时间间隔和关系表示。此外，可以在TM中以图形方式解决不完美间隔的时间查询，这比数学表达式更接近人类的直觉。由于人的思想在感知和处理图形表示上比在数字表示上更有效，因此我们相信TM可以用作分析和推理不完美的时间间隔的有价值的辅助工具。

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