Skip to main content

Conformance Relations for Fuzzy Automata

  • Conference paper
  • First Online:
Advances in Computational Intelligence (IWANN 2019)

Abstract

The use of formal methods improves the reliability of computer systems. In this context, fuzzy logic provides a tool to formally specify systems where uncertainty and imprecision play an important role. In this paper, we propose an extension of the fuzzy automata formalism and establish different conformance relations. The main goal of these relations is to formally capture the idea of a system behaving as specified by a specification. We sketch how our conformance relations can be alternatively characterized as a testing process by producing sound and complete sets of tests.

Research partially supported by the Spanish MINECO/FEDER project DArDOS (TIN2015-65845-C3-1-R and TIN2015-65845-C3-3-R) and the Comunidad de Madrid project FORTE-CM (S2018/TCS-4314).

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Ammann, P., Offutt, J.: Introduction to Software Testing, 2nd edn. Cambridge University Press, Cambridge (2017)

    Google Scholar 

  2. Andrés, C., Llana, L., Núñez, M.: Self-adaptive fuzzy-timed systems. In: 13th IEEE Congress on Evolutionary Computation, CEC 2011, pp. 115–122. IEEE Computer Society (2011)

    Google Scholar 

  3. Boubeta-Puig, J., Camacho, A., Llana, L., Núñez, M.: A formal framework to specify and test systems with fuzzy-time information. In: Rojas, I., Joya, G., Catala, A. (eds.) IWANN 2017. LNCS, vol. 10306, pp. 403–414. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59147-6_35

    Chapter  Google Scholar 

  4. Calvo, I., Merayo, M.G., Núñez, M.: An improved and tool-supported fuzzy automata framework to analyze heart data. In: Nguyen, N.T., Hoang, D.H., Hong, T.-P., Pham, H., Trawiński, B. (eds.) ACIIDS 2018. LNCS (LNAI), vol. 10751, pp. 694–704. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75417-8_65

    Chapter  Google Scholar 

  5. Camacho, A., Merayo, M.G., Núñez, M.: Using fuzzy automata to diagnose and predict heart problems. In 19th IEEE Congress on Evolutionary Computation, CEC 2017, pp. 846–853. IEEE Computer Society (2017)

    Google Scholar 

  6. Cavalli, A.R., Higashino, T., Núñez, M.: A survey on formal active and passive testing with applications to the cloud. Ann. Telecommun. 70(3–4), 85–93 (2015)

    Article  Google Scholar 

  7. Doostfatemeh, M., Kremer, S.C.: New directions in fuzzy automata. Int. J. Approximate Reasoning 38(2), 175–214 (2005)

    Article  MathSciNet  Google Scholar 

  8. Hierons, R.M., et al.: Using formal specifications to support testing. ACM Comput. Surv. 41(2), 9:1–9:76 (2009)

    Article  MathSciNet  Google Scholar 

  9. Lamport, L.: Who builds a house without drawing blueprints? Commun. ACM 58(4), 38–41 (2015)

    Article  Google Scholar 

  10. Merayo, M.G., Núñez, M., Rodríguez, I.: Formal testing from timed finite state machines. Comput. Netw. 52(2), 432–460 (2008)

    Article  Google Scholar 

  11. Mordeson, J.N., Malik, D.S.: Fuzzy Automata and Languages: Theory and Applications. Chapman & Hall/CRC (2002)

    Google Scholar 

  12. Shafique, M., Labiche, Y.: A systematic review of state-based test tools. Int. J. Softw. Tools Technol. Transf. 17(1), 59–76 (2015)

    Article  Google Scholar 

  13. Tretmans, J.: Model based testing with labelled transition systems. In: Hierons, R.M., Bowen, J.P., Harman, M. (eds.) Formal Methods and Testing. LNCS, vol. 4949, pp. 1–38. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78917-8_1

    Chapter  Google Scholar 

  14. Wee, W.G., Fu, K.S.: A formulation of fuzzy automata and its application as a model of learning systems. IEEE Trans. Syst. Sci. Cybern. 5(3), 215–223 (1969)

    Article  Google Scholar 

  15. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  Google Scholar 

  16. Zadeh, L.A.: Fuzzy sets, fuzzy logic, and fuzzy systems. In: Advances in Fuzzy Systems - Applications and Theory, vol. 6. World Scientific Press (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Manuel Núñez .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Calvo, I., Merayo, M.G., Núñez, M., Palomo-Lozano, F. (2019). Conformance Relations for Fuzzy Automata. In: Rojas, I., Joya, G., Catala, A. (eds) Advances in Computational Intelligence. IWANN 2019. Lecture Notes in Computer Science(), vol 11506. Springer, Cham. https://doi.org/10.1007/978-3-030-20521-8_62

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-20521-8_62

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-20520-1

  • Online ISBN: 978-3-030-20521-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics