Modelling and Computing with Imprecise and Uncertain Properties in Object Bases

  • Tru H. Cao
  • Hoa Nguyen
  • Ma Nam
Part of the Advances in Soft Computing book series (AINSC, volume 46)


Although fuzzy set and probability theories are complementary for dealing with pervasive imprecision and uncertainty in real world problems, object-oriented database models combining the relevance and strength of both the theories appear to be sporadic. This paper introduces our extension of Eiter et al.’s probabilistic object base model with two key features: (1) uncertain and imprecise attribute values are represented as probability distributions on a set of fuzzy set values; and (2) class methods with uncertain and imprecise input and output arguments are formally integrated into the new model. A probabilistic interpretation of relations on fuzzy set values is proposed for their combination with probability degrees. Then the syntax and semantics of fuzzy-probabilistic object base schemas, instances, and selection operation are defined. Furthermore, the soft computing paradigm needs to have real systems implemented to be useful in practice. This paper also presents our development of FPDB4O as a management system for fuzzy and probabilistic object bases of the proposed model.


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  1. 1.
    Baldwin, J.F., et al.: Toward soft computing object-oriented logic programming. In: Proceedings of the 9th IEEE International Conference on Fuzzy Systems, pp. 768–773 (2000)Google Scholar
  2. 2.
    Baldwin, J.F., Lawry, J.M., Martin, T.P.: A mass assignment theory of the probability of fuzzy events. International Journal of Fuzzy Sets and Systems 83, 353–367 (1996)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Baldwin, J.F., Lawry, J.M., Martin, T.P.: A note on probability/possibility consistency for fuzzy events. In: Proceedings of the 6th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp. 521–525 (1996)Google Scholar
  4. 4.
    Berzal, F., et al.: A framework to build fuzzy object-oriented capabilities over an existing database system. In: Ma, Z. (ed.) Advances in fuzzy object-oriented database: modeling and applications, pp. 177–205. Idea Group Publishing, USA (2005)Google Scholar
  5. 5.
    Blanco, I., et al.: Softening the object-oriented database model: imprecision, uncertainty and fuzzy types. In: Proceedings of the 1st International Joint Conference of the International Fuzzy Systems Association and the North American Fuzzy Information Processing Society, pp. 2323–2328 (2001)Google Scholar
  6. 6.
    Bordogna, G., Pasi, G., Lucarella, D.: A fuzzy object-oriented data model managing vague and uncertain information. International Journal of Intelligent Systems 14, 623–651 (1999)CrossRefGoogle Scholar
  7. 7.
    Cao, T.H.: Uncertain inheritance and recognition as probabilistic default reasoning. International Journal of Intelligent Systems 16, 781–803 (2001)MATHCrossRefGoogle Scholar
  8. 8.
    Cao, T.H., Nguyen, H.: Fuzzy and probabilistic object bases. In: Ma, Z. (ed.) Advances in fuzzy object-oriented databases: modelling and applications, pp. 46–84. Idea Group Publisher, USA (2005)Google Scholar
  9. 9.
    Cao, T.H., Rossiter, J.M.: A deductive probabilistic and fuzzy object-oriented database language. International Journal of Fuzzy Sets and Systems 140, 129–150 (2003)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Cross, V.V.: Defining fuzzy relationships in object models: Abstraction and interpretation. International Journal of Fuzzy Sets and Systems 140, 5–27 (2003)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    De Tré, G., De Caluwe, R.: A constraint based fuzzy object-oriented database model. In: Ma, Z. (ed.) Advances in fuzzy object-oriented databases: Modelling and applications, pp. 1–45. Idea Group Publisher, USA (2005)Google Scholar
  12. 12.
    Dubitzky, W., et al.: Towards concept-oriented databases. Data & Knowledge Engineering 30, 23–55 (1999)MATHCrossRefGoogle Scholar
  13. 13.
    Eiter, T., et al.: Probabilistic object bases. ACM Transactions on Database Systems 26, 264–312 (2001)CrossRefMATHGoogle Scholar
  14. 14.
    Gaines, B.R.: Fuzzy and probability uncertainty logics. Journal of Information and Control 38, 154–169 (1978)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    George, R., Buckles, B.P., Petry, F.E.: Modelling class hierarchies in the fuzzy object-oriented data model. International Journal of Fuzzy Sets and Systems 60, 259–272 (1993)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Grehan, R.: Complex object structures, persistence, and DB4O. Series of db4o whitepaper. db4objects Inc. (2005)Google Scholar
  17. 17.
    Klir, G.J., Yuan, B.: Fuzzy sets and fuzzy logic - theory and applications. Prentice Hall PTR, Englewood Cliffs (1995)MATHGoogle Scholar
  18. 18.
    Lakshmanan, L.V.S., et al.: ProbView: A flexible probabilistic database system. ACM Transactions on Database Systems 22, 419–469 (1997)CrossRefGoogle Scholar
  19. 19.
    Mohamedally, D., et al.: MIKE’s PET: A participant-based experiment tracking tool for HCI practitioners using mobile devices. In: Proceedings of SPIE’s 18th Annual Symposium for Electronic Imaging, pp. 216–224 (2006)Google Scholar
  20. 20.
    Nakada, H., et al.: Design and implementation of a local scheduling system with advance reservation for co-allocation on the grid. In: Proceedings of the 6th IEEE International Conference on Computer and Information Technology, pp. 217–222 (2006)Google Scholar
  21. 21.
    Pfeifer, D.: Flexible object-oriented views using method propagation. In: Proceedings of the 8th International Conference on Object-Oriented Information Systems, pp. 521–535 (2002)Google Scholar
  22. 22.
    Ross, R., Subrahmanian, V.S.: Aggregate Operators in Probabilistic Databases. Journal of the ACM 52, 54–101 (2005)CrossRefMathSciNetGoogle Scholar
  23. 23.
    Rossazza, J.-P., Dubois, D., Prade, H.: A hierarchical model of fuzzy classes. In: De Caluwe, R. (ed.) Fuzzy and uncertain object-oriented databases: Concepts and models, pp. 21–61. World Scientific, Singapore (1997)Google Scholar
  24. 24.
    Van Gyseghem, N., De Caluwe, R.: The UFO database model: Dealing with imperfect information. In: De Caluwe, R. (ed.) Fuzzy and uncertain object-oriented databases: Concepts and models, pp. 123–185. World Scientific, Singapore (1997)Google Scholar
  25. 25.
    Yazici, A., George, R.: Fuzzy database modelling. Studies in Fuzziness and Soft Computing, vol. 26. Physica-Verlag, Heidelberg (1999)Google Scholar
  26. 26.
    Zadeh, L.A.: PRUF - A meaning representation language for natural languages. International Journal of Man-Machine Studies 10, 395–460 (1978)MATHMathSciNetCrossRefGoogle Scholar
  27. 27.
    Zhang, X., et al.: A usage-based authorization framework for collaborative computing system. In: Proceedings of ACM Symposium on Access Control Models and Technologies, pp. 180–189 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Tru H. Cao
    • 1
  • Hoa Nguyen
    • 2
  • Ma Nam
    • 1
  1. 1.Ho Chi Minh City University of Technology 
  2. 2.Ho Chi Minh City Open University 

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