A Probabilistic Object-Oriented Database Model with Fuzzy Measures

  • Li Yan
  • Z. Ma
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 304)


This chapter concentrates on modeling probabilistic evens with fuzzy measures in the object-oriented databases. Instead of crisp probability measures or interval probability measures of objects and classes, fuzzy sets are applied to represent imprecise probability measures. A probabilistic object-oriented database model with fuzzy measures is introduced, which incorporates fuzzy probability degrees to handle imprecision and uncertainty. Based on the proposed probabilistic object-oriented database model, several major semantic relationships of probabilistic objects and probabilistic classes with fuzzy measures are investigated in the chapter.


Membership Degree Virtual Object Probabilistic Object Fuzzy Measure Possibility Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Baldwin, J.M., Lawry, J., 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, Granada, Spain, pp. 521–525 (July 1996)Google Scholar
  2. 2.
    Barbara, D., Garcia-Molina, H., Porter, D.: The management of probabilistic data. IEEE Transactions on Knowledge and Data Engineering 4(5), 487–502 (1992)CrossRefGoogle Scholar
  3. 3.
    Buckles, B.P., Petry, F.E.: A fuzzy representation of data for relational databases. Fuzzy Sets and Systems 7(3), 213–226 (1982)zbMATHCrossRefGoogle Scholar
  4. 4.
    Cao, T.H., Nguyen, H.: Uncertain and fuzzy object bases: a data model and algebraic operations, International Journal of Uncertainty. Fuzziness and Knowledge-Based Systems 19(2), 275–305 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Cao, T.H., Rossiter, J.M.: A deductive probabilistic and fuzzy object-oriented database language. Fuzzy Sets and Systems 140(1), 129–150 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Cavallo, R., Pittarelli, M.: The theory of probabilistic databases. In: Proceedings of the 13th VLDB Conference, Brighton, England, pp. 71–81 (September 1987)Google Scholar
  7. 7.
    de Tré, G., de Caluwe, R., Prade, H.: Null values in fuzzy databases. Journal of Intelligent Information Systems 30(2), 93–114 (2008)CrossRefGoogle Scholar
  8. 8.
    Dey, D., Sarkar, S.A.: Probabilistic relational model and algebra. ACM Transactions on Database Systems 21(3), 339–369 (1996)CrossRefGoogle Scholar
  9. 9.
    Eiter, T., Lu, J.J., Lukasiewicz, T., Subrahmanian, V.S.: Probabilistic object bases. ACM Transactions on Database Systems 26(3), 264–312 (2001)zbMATHCrossRefGoogle Scholar
  10. 10.
    Haas, P.J., Suciu, D.: Special issue on uncertain and probabilistic databases. The VLDB Journal 18(5), 987–988 (2009)CrossRefGoogle Scholar
  11. 11.
    Kornatzky, Y., Shimony, S.E.: A probabilistic object-oriented data model. Data & Knowledge Engineering 12(2), 143–166 (1994)CrossRefGoogle Scholar
  12. 12.
    Lakshmanan, L.V.S., Leone, N., Ross, R., Subrahmanian, V.S.: ProbView: a flexible probabilistic database system. ACM Transactions on Database Systems 22(3), 419–469 (1997)CrossRefGoogle Scholar
  13. 13.
    Ma, Z.M., Yan, L.: Updating extended possibility-based fuzzy relational databases. International Journal of Intelligent Systems 22(3), 237–258 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Ma, Z.M., Yan, L.: Fuzzy XML data modeling with the UML and relational data models. Data & Knowledge Engineering 63(3), 970–994 (2007)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Ma, Z.M., Yan, L.: A literature overview of fuzzy database models. Journal of Information Science and Engineering 24(1), 189–202 (2008)zbMATHGoogle Scholar
  16. 16.
    Ma, Z.M., Yan, L.: A literature overview of fuzzy conceptual data modeling. Journal of Information Science and Engineering 26(2), 427–441 (2010)Google Scholar
  17. 17.
    Ma, Z.M., Zhang, F., Yan, L.: Fuzzy information modeling in UML class diagram and relational database models. Applied Soft Computing 11(6), 4236–4245 (2011)CrossRefGoogle Scholar
  18. 18.
    Ma, Z.M., Zhang, W.J., Ma, W.Y.: Extending object-oriented databases for fuzzy information modeling. Information Systems 29(5), 421–435 (2004)CrossRefGoogle Scholar
  19. 19.
    Ma, Z.M., Yan, L.: Conflicts and their resolutions in fuzzy relational multidatabases. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 18(2), 169–195 (2010)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Nuray-Turan, R., Kalashnikov, D.V., Mehrotra, S., Yu, Y.M.: Attribute and object selection queries on objects with probabilistic attributes. ACM Transactions on Database Systems 37(1), 3 (2012)Google Scholar
  21. 21.
    Parsons, S.: Current approaches to handling imperfect information in data and knowledge bases. IEEE Transactions on Knowledge and Data Engineering 8(2), 353–372 (1996)CrossRefGoogle Scholar
  22. 22.
    Pittarelli, M.: An algebra for probabilistic databases. IEEE Transactions on Knowledge and Data Engineering 6(2), 293–303 (1994)CrossRefGoogle Scholar
  23. 23.
    Prade, H., Testemale, C.: Generalizing database relational algebra for the treatment of incomplete/uncertain information and vague queries. Information Sciences 34(2), 115–143 (1984)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Raju, K.V.S.V.N., Majumdar, A.K.: Fuzzy functional dependencies and lossless join decomposition of fuzzy relational database systems. ACM Transactions on Database Systems 13(2), 129–166 (1988)CrossRefGoogle Scholar
  25. 25.
    Umano, M., Fukami, S.: Fuzzy relational algebra for possibility-distribution-fuzzy-relational model of fuzzy data. Journal of Intelligent Information Systems 3(1), 7–27 (1994)CrossRefGoogle Scholar
  26. 26.
    Yan, L., Ma, Z.M.: Algebraic operations in fuzzy object-oriented databases. Information Systems Frontiers (2013), doi:10.1007/s10796-012-9359-8Google Scholar
  27. 27.
    Yang, Q., Zhang, W.N., Liu, C.W., Wu, J., Yu, C.T., Nakajima, H., Rishe, N.: Efficient processing of nested fuzzy SQL queries in a fuzzy database. IEEE Transactions on Knowledge and Data Engineering 13(6), 884–901 (2001)CrossRefGoogle Scholar
  28. 28.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Zadeh, L. A.: The concept of a linguistic variable and its application to approximate reasoning. Information Sciences 8 (3), 199–249, 8 (4), 301–357, 9(1): 43–80 (1975)Google Scholar
  30. 30.
    Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1(1), 3–28 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  31. 31.
    Zhang, W.N., Laun, E., Meng, W.Y.: A methodology of integrating fuzzy relational databases in a multidatabase system. In: Proceedings of the 5th International Conference on Database Systems for Advanced Applications, Melbourne, Australia, pp. 401–410 (April 1997)Google Scholar
  32. 32.
    Zimanyi, E.: Query evaluation in probabilistic relational databases. Theoretical Computer Science 171(1-2), 179–219 (1997)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Li Yan
    • 1
  • Z. Ma
    • 2
  1. 1.School of SoftwareNortheastern UniversityShenyangChina
  2. 2.School of Information Science & EngineeringNortheastern UniversityShenyangChina

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