A Generalized Approach for Determining Fuzzy Temporal Relations

  • Luyi Bai
  • Zongmin Ma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7389)


Fuzzy temporal relations have been defined to support temporal knowledge representation and reasoning in the presence of fuzziness, which are still open issues. In this paper, we propose a generalized approach for determining fuzzy temporal relations assuming that fuzzy temporal intervals are all fuzzy. We firstly present the basics of representation of fuzzy temporal relations from two aspects: fuzzy time point and fuzzy time interval, and then give definitions of their fuzzy relations. On this basis, correspondences between fuzzy and crisp temporal relations are investigated. Finally, a general formalized algorithm for determining fuzzy temporal relations is proposed.


Fuzzy time point Fuzzy time interval Fuzzy temporal relations 


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  1. 1.
    Allen, J.F.: Maintaining Knowledge about Temporal Intervals. Communications of ACM 26(11), 832–843 (1983)zbMATHCrossRefGoogle Scholar
  2. 2.
    Badaloni, S., Falda, M.: Classical and Fuzzy Neighborhood Relations of the Temporal Qualitative Algebra. In: Proceedings of the 16th International Symposium on Temporal Representation and Reasoning, pp. 147–154 (2009)Google Scholar
  3. 3.
    Badaloni, S., Giacomin, M.: The Algebra IAfuz: A Framework for Qualitative Fuzzy Temporal Reasoning. Artificial Intelligence 170(10), 872–908 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Barro, S., Marin, R., Mira, J., Paton, A.R.: Model and Language for the Fuzzy Representation and Handling of Time. Fuzzy Sets and System 61(2), 153–175 (1994)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Dubois, D., Fargier, H., Prade, H.: Possibility Theory in Constraint Satisfaction Problems: Handling Priority, Preference and Uncertainty. Applied Intelligence 6(4), 287–309 (1996)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Dubois, D., Prade, H.: Processing Fuzzy Temporal Knowledge. IEEE Transaction on System, Man and Cybernetics 19(4), 729–744 (1989)MathSciNetCrossRefGoogle Scholar
  7. 7.
    El-Kholy, A., Richards, B.: Temporal and Resource Reasoning in Planning: the parcPLAN Approach. In: Proceedings of the 12th European Conference on Artificial Intelligence (ECAI 1996), pp. 614–618 (1996)Google Scholar
  8. 8.
    Fox, M., Long, D.: PDDL2.1: An Extension to PDDL for Expressing Temporal Planning Domains. Journal of Artificial Intelligence Research 20, 61–124 (2003)zbMATHGoogle Scholar
  9. 9.
    Freksa, C.: Spatial and Temporal Structures in Cognitive Processes. In: Freksa, C., Jantzen, M., Valk, R. (eds.) Foundations of Computer Science. LNCS, vol. 1337, pp. 379–387. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  10. 10.
    Harabagiu, S., Bejan, C.: Question Answering Based on Temporal Inference. In: AAAI 2005 Workshop on Inference for Textual Question Answering, Pittsburgh, PA (2005)Google Scholar
  11. 11.
    Jonsson, P., Bäckström, C.: A Unifying Approach to Temporal Constraint Reasoning. Artificial Intelligence 102(1), 143–155 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Kautz, H., Ladkin, P.: Integrating Metric and Qualitative Temporal Reasoning. In: The 9th National Conference on Artificial Intelligence, pp. 241–246 (1991)Google Scholar
  13. 13.
    Koubarakis, M.: Tractable Disjunctions of Linear Constraints: Basic Results and Applications to Temporal Reasoning. Theoretical Computer Science 266(1), 311–339 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Meiri, I.: Combining Qualitative and Quantitative Constraints in Temporal Reasoning. Artificial Intelligence 87(1), 343–385 (1996)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Navarrete, I., Sattar, A., Wetprasit, R., Marin, R.: On Point-Duration Networks for Temporal Reasoning. Artificial Intelligence 140(1-2), 39–70 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Ribarić, S., Bašić, B.D., Maleš, L.: An Approach to Validation of Fuzzy Qualitative Temporal Relations. In: Proceedings of the 24th International Conference on Information Technology Interfaces, pp. 223–228 (2002)Google Scholar
  17. 17.
    Sanampudi, S.K., Kumari, G.V.: Temporal Reasoning in Natural Language Processing: A Survey. International Journal of Computer Applications 1(4), 53–57 (2010)CrossRefGoogle Scholar
  18. 18.
    Schockaert, S., De Cock, M.: Temporal Reasoning about Fuzzy Intervals. Artificial Intelligence 172(8-9), 1158–1193 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Schockaert, S., De Cock, M., Kerre, E.E.: An Efficient Characterization of Fuzzy Temporal Interval Relations. In: Proceedings of the IEEE International Conference on Fuzzy Systems, pp. 1894–1901 (2006)Google Scholar
  20. 20.
    Zadeh, L.A.: Fuzzy Sets. Information and Control 8(4), 338–353 (1965)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Zadeh, L.A.: Fuzzy Sets as a Basis for Theory of Possibility. Fuzzy Sets and Systems 1(1), 3–28 (1978)MathSciNetzbMATHCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Luyi Bai
    • 1
  • Zongmin Ma
    • 1
  1. 1.College of Information Science & EngineeringNortheastern UniversityShenyangChina

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