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Modelling imperfect time intervals in a two-dimensional space

Yi Qiang (UGent), Matthias Delafontaine (UGent), Katrin Asmussen (UGent), Birger Stichelbaut (UGent), Guy De Tré (UGent), Philippe De Maeyer (UGent) and Nico Van de Weghe (UGent)
(2010) CONTROL AND CYBERNETICS. 39(4). p.983-1010
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Abstract
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 (TM), 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.
Keywords
fuzzy time interval, the Triangular Model, fuzzy set, rough time interval, FUZZY INTERVALS, rough set, temporal relation

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Chicago
Qiang, Yi, Matthias Delafontaine, Katrin Asmussen, Birger Stichelbaut, Guy De Tré, Philippe De Maeyer, and Nico Van de Weghe. 2010. “Modelling Imperfect Time Intervals in a Two-dimensional Space.” Control and Cybernetics 39 (4): 983–1010.
APA
Qiang, Yi, Delafontaine, M., Asmussen, K., Stichelbaut, B., De Tré, G., De Maeyer, P., & Van de Weghe, N. (2010). Modelling imperfect time intervals in a two-dimensional space. CONTROL AND CYBERNETICS, 39(4), 983–1010.
Vancouver
1.
Qiang Y, Delafontaine M, Asmussen K, Stichelbaut B, De Tré G, De Maeyer P, et al. Modelling imperfect time intervals in a two-dimensional space. CONTROL AND CYBERNETICS. 2010;39(4):983–1010.
MLA
Qiang, Yi, Matthias Delafontaine, Katrin Asmussen, et al. “Modelling Imperfect Time Intervals in a Two-dimensional Space.” CONTROL AND CYBERNETICS 39.4 (2010): 983–1010. Print.
@article{1167612,
  abstract     = {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 (TM), 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.},
  author       = {Qiang, Yi and Delafontaine, Matthias and Asmussen, Katrin and Stichelbaut, Birger and De Tr{\'e}, Guy and De Maeyer, Philippe and Van de Weghe, Nico},
  issn         = {0324-8569},
  journal      = {CONTROL AND CYBERNETICS},
  keyword      = {fuzzy time interval,the Triangular Model,fuzzy set,rough time interval,FUZZY INTERVALS,rough set,temporal relation},
  language     = {eng},
  number       = {4},
  pages        = {983--1010},
  title        = {Modelling imperfect time intervals in a two-dimensional space},
  volume       = {39},
  year         = {2010},
}

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