Skip to main content
SpringerLink
Log in

Modeling and Specification of Nondeterministic Fuzzy Discrete-Event Systems

  • Chapter
  • First Online:
Decision Making under Constraints

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 276))

Abstract

Most of the published research on fuzzy discrete-event systems (FDESs) has focused on systems that are modeled as deterministic fuzzy automata. In fact, nondeterminism in FDESs occurs in many practical situations and can be used to represent underspecification or incomplete information. In this paper, we pay attention to the modeling and specification of nondeterministic FDESs (NFDESs). We model NFDESs by a new kind of fuzzy automata. To describe adequately the behavior of NFDESs, we introduce the concept of bisimulation, which is a finer behavioral measure than fuzzy language equivalence. Further, we propose the notion of nondeterministic fuzzy specifications (NFSs) to specify the behavior of NFDESs and introduce a satisfaction relation between NFDESs and NFSs. If such a relation exists, then at least one knows that there is no unwanted behavior in the system.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Benmessahel, B., Touahria, M., Nouioua, F., Gaber, J., Lorenz, P.: Decentralized prognosis of fuzzy discrete-event systems. Iran. J. Fuzzy Syst. 16(3), 127–143 (2019)

    Google Scholar 

  2. Cao, Y., Chen, G., Kerre, E.: Bisimulations for fuzzy-transition systems. IEEE Trans. Fuzzy Syst. 19(3), 540–552 (2011)

    Article  Google Scholar 

  3. Cao, Y., Ezawa, Y.: Nondeterministic fuzzy automata. Inform. Sci. 191, 86–97 (2012)

    Article  MathSciNet  Google Scholar 

  4. Cao, Y., Sun, S.X., Wang, H., Chen, G.: A behavioral distance for fuzzy transition systems. IEEE Trans. Fuzzy Syst. 21(4), 735–747 (2013)

    Article  Google Scholar 

  5. Cao, Y., Ying, M.: Supervisory control of fuzzy discrete event systems. IEEE Trans. Syst. Man Cybern. B Cybern. 35(2), 366–371 (2005)

    Google Scholar 

  6. Cao, Y., Ying, M.: Observability and decentralized control of fuzzy discrete-event systems. IEEE Trans. Fuzzy Syst. 14(2), 202–216 (2006)

    Article  MathSciNet  Google Scholar 

  7. Cao, Y., Ying, M., Chen, G.: State-based control of fuzzy discrete-event systems. IEEE Trans. Syst. Man Cybern. B Cybern. 37(2), 410–424 (2007)

    Google Scholar 

  8. Chen, T., Han, T., Cao, Y.: Polynomial-time algorithms for computing distances of fuzzy transition systems. Theor. Comput. Sci. 727, 24–36 (2018)

    Article  MathSciNet  Google Scholar 

  9. Ćirić, M., Stamenković, A., Ignjatović, J., Petković, T.: Fuzzy relation equations and reduction of fuzzy automata. J. Comput. Syst. Sci. 76(7), 609–633 (2010)

    Article  MathSciNet  Google Scholar 

  10. Deng, W., Qiu, D.: State-based decentralized diagnosis of bi-fuzzy discrete event systems. IEEE Trans. Fuzzy Syst. 25(4), 3854–867 (2017)

    Google Scholar 

  11. Du, X., Ying, H., Lin, F.: Theory of extended fuzzy discrete-event systems for handling ranges of knowledge uncertainties and subjectivity. IEEE Trans. Fuzzy Syst. 17(2), 316–328 (2009)

    Article  Google Scholar 

  12. Garg, V.K., Kumar, R., Marcus, S.I.: A probabilistic language formalism for stochastic discrete-event systems. IEEE Trans. Automat. Contr. 44(2), 280–293 (1999)

    Article  MathSciNet  Google Scholar 

  13. Heymann, M., Lin, F.: Discrete-event control of nondeterministic systems. IEEE Trans. Automat. Contr. 43(1), 3–17 (1998)

    Article  MathSciNet  Google Scholar 

  14. Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall, Englewood Cliffs, NJ (1985)

    MATH  Google Scholar 

  15. Huq, R., Mann, G.K.I., Gosine, R.G.: Behavior-modulation technique in mobile robotics using fuzzy discrete event system. IEEE Trans. Robot. 22(5), 903–916 (2006)

    Article  Google Scholar 

  16. Jiang, S., Kumar, R.: Supervisory control of nondeterministic discrete-event systems with driven events via masked prioritized synchronization. IEEE Trans. Automat. Contr. 47(9), 1438–1449 (2002)

    Article  MathSciNet  Google Scholar 

  17. Kumar, R., Garg, V.K.: Control of stochastic discrete event systems modeled by probabilistic languages. IEEE Trans. Automat. Contr. 46(4), 593–606 (2001)

    Article  MathSciNet  Google Scholar 

  18. Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Inform. Comput. 94, 1–28 (1991)

    Article  MathSciNet  Google Scholar 

  19. Lawford, M., Wonham, W.M.: Supervisory control of probabilistic discrete event systems. In: Proceedings of 36th Midwest Symposium on Circuits and Systems, vol. 1, pp. 327–331. IEEE, Detroit, MI (1993)

    Google Scholar 

  20. Li, Y.H., Lin, F., Lin, Z.H.: Supervisory control of probabilistic discrete-event systems with recovery. IEEE Trans. Automat. Contr. 44(10), 1971–1975 (1999)

    Article  MathSciNet  Google Scholar 

  21. Lin, F., Ying, H.: Modeling and control of fuzzy discrete event systems. IEEE Trans. Syst. Man Cybern. B Cybern. 32(4), 408–415 (2002)

    Google Scholar 

  22. Lin, F., Ying, H.: State-feedback control of fuzzy discrete-event systems. IEEE Trans. Syst. Man Cybern. B Cybern. 40(3), 951–956 (2010)

    Google Scholar 

  23. Lin, F., Ying, H., MacArthur, R.D., Cohn, J.A., Barth-Jones, D., Crane, L.R.: Decision making in fuzzy discrete event systems. Inform. Sci. 177(18), 3749–3763 (2007)

    Article  Google Scholar 

  24. Liu, J.P., Li, Y.M.: The relationship of controllability between classical and fuzzy discrete-event systems. Inform. Sci. 178(21), 4142–4151 (2008)

    Article  MathSciNet  Google Scholar 

  25. Liu, R., Wang, Y.X., Zhang, L.: An FDES-based shared control method for asynchronous brain-actuated robot. IEEE Trans. Cybern. 46(6), 1452–1462 (2016)

    Article  Google Scholar 

  26. Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs, New Jersey (1989)

    MATH  Google Scholar 

  27. Pantelic, V., Postma, S.M., Lawford, M.: Probabilistic supervisory control of probabilistic discrete event systems. IEEE Trans. Automat. Contr. 54(8), 2013–2018 (2009)

    Article  MathSciNet  Google Scholar 

  28. Park, D.: Concurrency and automata on infinite sequences. In: Proceedings of 5th GI-Conference Theoretical Computer Science. Lecture Notes in Computer Science, vol. 104, pp. 167–183. Springer (1981)

    Google Scholar 

  29. Petković, T.: Congruences and homomorphisms of fuzzy automata. Fuzzy Sets Syst. 157, 444–458 (2006)

    Article  MathSciNet  Google Scholar 

  30. Qiu, D.W.: Supervisory control of fuzzy discrete event systems: a formal approach. IEEE Trans. Syst. Man Cybern. B Cybern. 35(1), 72–88 (2005)

    Google Scholar 

  31. Qiu, D.W., Liu, F.C.: Fuzzy discrete-event systems under fuzzy observability and a test algorithm. IEEE Trans. Fuzzy Syst. 17(3), 578–589 (2009)

    Article  Google Scholar 

  32. Sun, D.D., Li, Y.M., Yang, W.W.: Bisimulation relations for fuzzy finite automata. Fuzzy Syst. Math. 23, 92–100 (2009). (in Chinese)

    Google Scholar 

  33. de Vink, E.P., Rutten, J.J.M.M.: Bisimulation for probabilistic transition systems: a coalgebraic approach. Theor. Comput. Sci. 221, 271–293 (1999)

    Article  MathSciNet  Google Scholar 

  34. Wonham, W.M.: Supervisory control of discrete-event systems. University of Toronto, Toronto, ON, Canada, Technical Report (2005). http://www.control.utoronto.ca/DES/

  35. Ying, H., Lin, F., MacArthur, R.D., Cohn, J.A., Barth-Jones, D.C., Ye, H., Crane, L.R.: A fuzzy discrete event system approach to determining optimal HIV/AIDS treatment regimens. IEEE Trans. Inform. Tech. Biomed. 10(4), 663–676 (2006)

    Article  Google Scholar 

  36. Ying, H., Lin, F., MacArthur, R.D., Cohn, J.A., Barth-Jones, D.C., Ye, H., and L. R. Crane, “A self-learning fuzzy discrete event system for HIV/AIDS treatment regimen selection. IEEE Trans. Syst. Man Cybern. B Cybern. 37(4), 966–979 (2007)

    Google Scholar 

  37. Zhou, C., Kumar, R., Jiang, S.: Control of nondeterministic discrete-event systems for bisimulation equivalence. IEEE Trans. Automat. Contr. 51(5), 754–765 (2006)

    Article  MathSciNet  Google Scholar 

  38. Zhou, C., Kumar, R.: Control of nondeterministic discrete event systems for simulation equivalence. IEEE Trans. Automat. Sci. Eng. 4(3), 340–349 (2007)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 61672023, 61772035, and 61751210, Guangxi Natural Science Foundation of China under Grant 2018GXNSFAA281326, and Guangxi Key Laboratory of Trusted Software under Grant kx201911.

Author information

Authors and Affiliations

  1. Key Laboratory of High Confidence Software Technologies (MOE), Department of Computer Science and Technology, Peking University, Beijing, 100871, China

    Yongzhi Cao

  2. Faculty of Informatics, Kansai University, Osaka, 569-1095, Japan

    Yoshinori Ezawa

  3. School of Economics and Management, Tsinghua University, Beijing, 100084, China

    Guoqing Chen

  4. Guangxi Key Laboratory of Trusted Software, Guilin University of Electronic Technology, Guilin, 541004, China

    Haiyu Pan

Authors
  1. Yongzhi Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yoshinori Ezawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guoqing Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Haiyu Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongzhi Cao .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Martine Ceberio

  2. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Vladik Kreinovich

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Cao, Y., Ezawa, Y., Chen, G., Pan, H. (2020). Modeling and Specification of Nondeterministic Fuzzy Discrete-Event Systems. In: Ceberio, M., Kreinovich, V. (eds) Decision Making under Constraints. Studies in Systems, Decision and Control, vol 276. Springer, Cham. https://doi.org/10.1007/978-3-030-40814-5_6

Download citation

Publish with us

Policies and ethics

Search

Navigation