Modeling and Verifying Imprecise Requirements of Systems Using Event-B

  • Hong Anh LeEmail author
  • Loan Dinh Thi
  • Ninh Thuan Truong
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 244)


Formal methods are mathematical techniques for describing system model properties. Such methods providing frameworks to specify and verify the correctness of systems which are usually described by precise requirements. In fact, system requirements are sometimes described with vague, imprecise, uncertain, ambiguous, or probabilistic terms. In this paper, we propose an approach to model and verify software systems with imprecise requirements using a formal method, e.g. Event-B. In the first step, we generalize our approach by representing some fuzzy concepts in the classical set theory. We then use such definitions to formalize the fuzzy requirements in Event-B and finally verify its properties such as safety, inconsistency and redundancy by using the Rodin tool. We also take a case study to illustrate the approach in detail.


Fuzzy Logic Formal Method Safety Property Proof Obligation Fuzzy Concept 
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.
    B method web site,
  2. 2.
    Event-b and the rodin platform,
  3. 3.
    Fuzzytech home page (2012),
  4. 4.
    Prevention of load sway by a fuzzy controller (2013),
  5. 5.
    Set operations (2013),
  6. 6.
    Aziz, M.H., Bohez, E.L.J., Parnichkun, M., Saha, C.: Classification of fuzzy petri nets, and their applications. Engineering and Technology, World Academy of Science 72, 394–407 (2011)Google Scholar
  7. 7.
    Goncalves, M., Rodríguez, R., Tineo, L.: Formal method to implement fuzzy requirements. RASI 9(1), 15–24 (2012)Google Scholar
  8. 8.
    Hoang, T.S., Iliasov, A., Silva, R., Wei, W.: A survey on event-b decomposition. ECEASST, Automated Verification of Critical Systems 46 (2011)Google Scholar
  9. 9.
    Intrigila, B., Magazzeni, D., Melatti, I., Tronci, E.: A model checking technique for the verification of fuzzy control systems. In: CIMCA 2005: Proceedings of the International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC 2006), vol. 1, pp. 536–542. IEEE Computer Society, Washington, DC (2005)Google Scholar
  10. 10.
    Knybel, J., Pavliska, V.: Representation of fuzzy if-then rules by petri nets. In: ASIS 2005, Prerov, Ostrava, pp. 121–125 (September 2005)Google Scholar
  11. 11.
    Lee, J., FanJiang, Y.-Y., Kuo, J.-Y., Lin, Y.-Y.: Modeling imprecise requirements with xml. In: Proceedings of the 2002 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2002, vol. 2, pp. 861–866 (2002)Google Scholar
  12. 12.
    Lee, J., Xue, N.-L., Hsu, K.-H., Yang, S.J.: Modeling imprecise requirements with fuzzy objects. Inf. Sci. 118(1-4), 101–119 (1999)CrossRefGoogle Scholar
  13. 13.
    Matthews, C., Swatman, P.A.: Fuzzy concepts and formal methods: A fuzzy logic toolkit for z. In: Bowen, J.P., Dunne, S., Galloway, A., King, S. (eds.) ZB 2000. LNCS, vol. 1878, pp. 491–510. Springer, Heidelberg (2000)Google Scholar
  14. 14.
    Matthews, C., Swatman, P.A.: Fuzzy concepts and formal methods: some illustrative examples. In: Proceedings of the Seventh Asia-Pacific Software Engineering Conference, APSEC 2000, pp. 230–238. IEEE Computer Society, Washington, DC (2000)CrossRefGoogle Scholar
  15. 15.
    Pavliska, V.: Petri nets as fuzzy modeling tool. Technical report, University of Ostrava - Institute for Research and Applications of Fuzzy Modeling (2006)Google Scholar
  16. 16.
    Yang, S.J.H., Tsai, J.J.P., Chen, C.-C.: Fuzzy rule base systems verification using high-level petri nets. IEEE Trans. Knowl. Data Eng. 15(2), 457–473 (2003)CrossRefGoogle Scholar
  17. 17.
    Zhong, Y.: The design of a controller in fuzzy petri net. Fuzzy Optimization and Decision Making 7, 399–408 (2008)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Hong Anh Le
    • 1
    Email author
  • Loan Dinh Thi
    • 2
  • Ninh Thuan Truong
    • 2
  1. 1.Hanoi University of Mining and GeologyHanoiVietnam
  2. 2.VNU - University of Engineering and TechnologyHanoiVietnam

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