Advertisement

Modeling Probabilistic Data with Fuzzy Probability Measures in UML Class Diagrams

  • Jie Sheng
  • Li YanEmail author
  • Zongmin Ma
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1000)

Abstract

Being a standard of the Object Management Group (OMG), the Unified Modeling Language (UML) has been applied to diverse domains. UML class diagram model is a conceptual data model and has been widely used for database design and information modeling. Information in real-world applications is often uncertain. To model and deal with uncertain data, various uncertain databases are pro-posed, including fuzzy ones and probabilistic ones. Also, there are few efforts in modeling fuzzy and probabilistic data in databases. But few efforts have been made on modeling uncertainty in conceptual data models. In this paper, we concentrate on modeling probabilistic data with fuzzy probability measures in the UML class diagram model. We introduce the semantics of fuzzy and probabilistic information into the UML class diagram model and extend several major constructs of UML class diagrams accordingly. We present the corresponding graph-ical representations of the extended UML class diagram model in the paper.

Notes

Acknowledgment

The work was supported in part by the National Natural Science Foundation of China (61772269 and 61370075).

References

  1. 1.
    Booch, G., Rumbaugh, J., Jacobson, I.: The Unified Modeling Language User Guide. Addison-Welsley Longman, Inc. (1998)Google Scholar
  2. 2.
    Object Management Group (OMG), Unified Modeling Language (UML), version 1.5, Technical report, OMG (2003). www.omg.org
  3. 3.
    Berardi, D., Calvanese, D., De Giacomo, G.: Reasoning on UML class diagrams. Artif. Intell. 168(1–2), 70–118 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Marcos, E., Vela, B., Cavero, J.M.: Extending UML for object-relational database design. In: Proceedings of the 4th International Conference on the Unified Modeling Language, Modeling Languages, Concepts, and Tools, pp. 225–239 (2001)zbMATHCrossRefGoogle Scholar
  5. 5.
    Ambler, S.W.: The Design of a Robust Persistence Layer for Relational Databases (2000). http://www.ambysoft.com/persistenceLayer.pdf
  6. 6.
    Conrad, R., Scheffiner, D., Freytag, J.C.: XML conceptual modeling using UML. In: Proceeding of the 19th International Conference on Conceptual Modeling, pp. 558–571 (2000)CrossRefGoogle Scholar
  7. 7.
    Falkovych, K., Sabou, M., Stuckenschmidt, H.: UML for the semantic web: transformation-based approaches. In: Knowledge Transformation for the Semantic Web. IOS Press (2003)Google Scholar
  8. 8.
    Parsons, S.: Current approaches to handling imperfect information in data and knowledge Bases. IEEE Trans. Knowl. Data Eng. 8(3), 353–372 (1996)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)zbMATHCrossRefGoogle Scholar
  10. 10.
    de Tr, G., de Caluwe, R., Prade, H.: Null values in fuzzy databases. J. Intell. Inf. Syst. 30(2), 93–114 (2008)CrossRefGoogle Scholar
  11. 11.
    Ma, Z.M., Zhang, W.J., Ma, W.Y.: Extending object-oriented databases for fuzzy information modeling. Inf. Syst. 29(5), 421–435 (2004)CrossRefGoogle Scholar
  12. 12.
    Cuevas, L., et al.: pg4DB: a fuzzy object-relational system. Fuzzy Sets Syst. 159(12), 1500–1514 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Ma, Z., Yan, L.: Modeling fuzzy data with XML: a survey. Fuzzy Sets Syst. 301, 146–159 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Lakshmanan, L.V.S., et al.: ProbView: a flexible probabilistic database system. ACM Trans. Database Syst. 22(3), 419–469 (1997)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Eiter, T., et al.: Probabilistic object bases. ACM Trans. Database Syst. 26(3), 264–312 (2001)zbMATHCrossRefGoogle Scholar
  16. 16.
    Kimelfeld, B., Senellart, P.: Probabilistic XML: models and complexity. In: Advances in Probabilistic Databases for Uncertain Information Management, pp. 39–66. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  17. 17.
    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 1996Google Scholar
  18. 18.
    Buckley, J.J.: Fuzzy Probabilities: New Approach and Applications. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  19. 19.
    Ralescu, A.: Fuzzy probabilities and their applications to statistical inference. In: Proceedings of the 5th International Conference on Processing and Management of Un-certainty in Knowledge-Based Systems, pp. 217–222 (1994)CrossRefGoogle Scholar
  20. 20.
    Rebiasz, B.: New methods of probabilistic and possibilistic interactive data processing. J. Intell. Fuzzy Syst. 30(5), 2639–2656 (2016)zbMATHCrossRefGoogle Scholar
  21. 21.
    Zadeh, L.A.: Fuzzy pobabilities. Inf. Process. Manag. 20(3), 363–372 (1984)CrossRefGoogle Scholar
  22. 22.
    Cao, T.H., Nguyen, H.: Uncertain and fuzzy object bases: a data model and alge-braic operations. Int. J. Uncertainty Fuzziness Knowl.-Based Syst. 19(2), 275–305 (2011)CrossRefGoogle Scholar
  23. 23.
    Cao, T.H., Rossiter, J.M.: A deductive probabilistic and fuzzy object-oriented da-tabase language. Fuzzy Sets Syst. 140(1), 129–150 (2003)zbMATHCrossRefGoogle Scholar
  24. 24.
    Yan, L., Ma, Z.M.: A fuzzy probabilistic relational database model and algebra. Int. J. Fuzzy Syst. 15(2), 244–253 (2013)Google Scholar
  25. 25.
    Yan, L., Ma, Z.: A probabilistic object-oriented database model with fuzzy measures and its algebraic operations. J. Intell. Fuzzy Syst. 28(5), 1969–1984 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Ma, Z., Li, C., Yan, L.: Reengineering probabilistic relational da-tabases with fuzzy probability measures into XML model. J. Database Manag. 28(3), 26–47 (2017)CrossRefGoogle Scholar
  27. 27.
    Zvieli, A., Chen, P.P.: Entity-relationship modeling and fuzzy databases. In: Proceedings of the 2nd IEEE International Conference on Data Engineering, pp. 320–327 (1986)Google Scholar
  28. 28.
    Chaudhry, N.A., Moyne, J.R., Rundensteiner, E.A.: An extended database design methodology for uncertain data management. Inf. Sci. 121(1–2), 83–112 (1999)CrossRefGoogle Scholar
  29. 29.
    Chen, G.Q., Kerre, E.E.: Extending ER/EER concepts towards fuzzy conceptual data modeling. In: Proceedings of the 7th IEEE International Conference on Fuzzy Systems, pp. 1320–1325 (1998)Google Scholar
  30. 30.
    Galindo, J., et al.: Relaxing constraints in enhanced entity-relationship models using fuzzy quantifiers. IEEE Trans. Fuzzy Syst. 12(6), 780–796 (2004)CrossRefGoogle Scholar
  31. 31.
    Ma, Z.M., et al.: Conceptual design of fuzzy object-oriented databases using extended entity-relationship model. Int. J. Intell. Syst. 16(6), 697–711 (2001)zbMATHCrossRefGoogle Scholar
  32. 32.
    Yan, L., Ma, Z.M.: Modeling fuzzy information in fuzzy extended entity-relationship model and fuzzy relational databases. J. Intell. Fuzzy Syst. 27(4), 1881–1896 (2014)MathSciNetzbMATHGoogle Scholar
  33. 33.
    Yan, L., Ma, Z.M.: Formal translation from fuzzy EER model to fuzzy XML model. Expert Syst. Appl. 41(8), 3615–3627 (2014)CrossRefGoogle Scholar
  34. 34.
    Ma, Z.M., Zhang, F., Yan, L.: Fuzzy information modeling in UML class diagram and relational database models. Appl. Soft Comput. 11(6), 4236–4245 (2011)CrossRefGoogle Scholar
  35. 35.
    Ma, Z.M., Yan, L., Zhang, F.: Modeling fuzzy information in UML class diagrams and object-oriented database models. Fuzzy Sets Syst. 186(1), 26–46 (2012)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Ma, Z.M., Yan, L.: Fuzzy XML data modeling with the UML and relational data models. Data Knowl. Eng. 63(3), 970–994 (2007)CrossRefGoogle Scholar
  37. 37.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8(3), 199–249 (1975); 8(4), 301–357 (1975); 9(1), 43–80 (1975)MathSciNetzbMATHCrossRefGoogle Scholar
  38. 38.
    Ma, Z.M., Zhang, W.J., Ma, W.Y.: Semantic measure of fuzzy data in extended possibility-based fuzzy relational databases. Int. J. Intell. Syst. 15(8), 705–716 (2000)zbMATHCrossRefGoogle Scholar
  39. 39.
    Teorey, T.J., Yang, D.Q., Fry, J.P.: A logical design methodology for relational databases using the extended entity-relationship model. ACM Comput. Surv. 18(2), 197–222 (1986)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.College of Computer Science and TechnologyNanjing University of Aeronautics and AstronauticsNanjingChina

Personalised recommendations