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Modelling imperfect time intervals in a two-dimensional space

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EN
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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 (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.
Rocznik
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983--1010
Opis fizyczny
Bibliogr. 32 poz., rys., wykr.
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Bibliografia
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  • BASSIRI, A., MALEK, M., ALESHEIKH, A. and AMIRIAN, P. (2009) Temporal Relationships between Rough Time Intervals. Computational Science and Its Applications - ICCSA 2009, 543-552.
  • BlTTNER, T. (2002) Approximate Qualitative Temporal Reasoning. Annals of Mathematics and Artificial Intelligence 36 (1), 39-80.
  • DE CALUWE, R., VAN DER CRUYSSEN, B., DE TRÉ, G., DEVOS, F. and MAESFRANCKX, P. (1999) The Semantics and Modelling of Flexible Time Indications. Computing with Words in Information/Intelligent Systems 1 (Foundations), Springer/Physica-Verlag, 229-256.
  • DE CALUWE, R., VAN DER CRUYSSEN, B., DE TRÉ, G., DEVOS, F. and MAESFRANCKX, P. (1997) Fuzzy Time Indications in Natural Language Interfaces. Flexible Query Answering Systems, Kluwer Academic Publishers, 163-185.
  • DE TRÉ, G., VAN DE WEGHE, N., DE CALUWE, R. and DE MAEYER, P. (2006) Towards a Flexible Visualization Tool for Dealing with Temporal Data. Flexible Query Answering Systems, 109-120.
  • DUBOIS, D. and PRADE, H. (2000) Fundamentals of Fuzzy Sets. Boston, USA, Kluwer Academic Publisher.
  • DUBOIS, D., HADJALI, A. and PRADE, H. (2003) Fuzziness and Uncertainty in Temporal Reasoning. Journal of Universal Computer Science 9 (9), 1168-1194.
  • DUBOIS, D., LANG, J. and PRADE, H. (1991) Timed Possibilistic Logic. Fundamenta Informaticae 15 (3-4), 211-234.
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  • GARRIDO, C., MARIN, N. and PONS, O. (2009) Fuzzy Intervals of Represent Fuzzy Valid Time in a Temporal Relational Database. International J. of Uncertainty, Fuzziness and Knowledge-Based Systems 17 (1), 173-192.
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  • KULPA, Z. (1997a) Diagrammatic Representation for a Space of Intervals. Machine Graphics & Vision 6, 5-24.
  • KULPA, Z. (1997b) Diagrammatic Representation of Interval Space in Proving Theorems About Interval Relations. Reliable Computing 3 (3), 209-217.
  • KULPA, Z. (2006) A Diagrammatic Approach to Investigate Interval Relations. Journal of Visual Languages and Computing 17 (5), 466-502.
  • LADKIN, P.B. (1987) The Logic of Time Representation. Ph.D. Dissertation. University of California, Berkeley. AAI8813947.
  • LIN, Y. (1991) Two Theories of Time. Journal of Applied Non-Classical Logics 1 (1), 37-63.
  • LONGLEY, P.A., GOODCHILD, M.F., MAGUIRE, D.J. and RHIND, D.W. (2001) Geographic Information Systems and Science, Chichester, England, John Wiley & Sons, Ltd.
  • NAGYPAL, G. and MOTIK, B. (2003) A Fuzzy Model for Representing Uncertain, Subjective, and Vague Temporal Knowledge in Ontologies. On the Move to Meaningful Internet Systems 2003: Coopis, Doa, and Odbase, 906-923.
  • OHLBACH, H.J. (2004) Relations between Fuzzy Time Intervals. Proceedings of the 11th International Symposium on Temporal Representation and Reasoning (Time 2004), Montreal, Canada. IEEE Computer Society.
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  • PAWLAK, Z. (1991) Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers.
  • SCHOCKAERT, S. and DE COCK, M. (2008) Temporal Reasoning About Fuzzy Intervals. Artificial Intelligence 172 (8-9), 1158-1193.
  • SCHOCKAERT, S., DE COCK, M. and KERRE, E.E. (2008) Fuzzifying Allen’s Temporal Interval Relations. IEEE Transactions on Fuzzy Systems 16 (2), 517-533.
  • SHOHAM, Y. and GOYAL, N. (1988) Temporal Reasoning in Artificial Intelligence. Exploring Artificial Intelligence, Morgan Kaufmann Publishers Inc., 419-438.
  • VAN DE WEGHE, N., DOCTER, R., DE MAEYER, P., BECHTOLD, B. and RYCKBOSCH, K. (2007) The Triangular Model as an Instrument for Visualising and Analysing Residuality. Journal of Archaeological Science 34 (4), 649-655.
  • VILA, L. (1994) A Survey on Temporal Reasoning in Artificial Intelligence. AI Commun. 7 (1), 4-28.
  • ZADEH, L.A. (1996a) Fuzzy Logic and Approximate Reasoning. Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers by Lotfi A. Zadeh, World Scientific Publishing Co., Inc., 238-259.
  • ZADEH, L.A. (1996b) Fuzzy Sets. Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers by Lotfi A. Zadeh, World Scientific Publishing Co., Inc., 19-34.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0060-0012
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