Skip to main content

Fuzziness in Automata Theory: Why? How?

  • Chapter
On Fuzziness

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 298))

Abstract

The aim of this article is to explain why we study fuzzy automata and how we do it, i.e., to highlight the most efficient tools of the theory of fuzzy sets that we use in our research. In addition, we want to show how research in the theory of fuzzy automata affected our research in other areas of the theory of fuzzy sets.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bělohlávek, R.: Determinism and Fuzzy Automata. Information Sciences 143, 205–209 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ćirić, M., Droste, M., Ignjatović, J., Vogler, H.: Determinization of Weighted Finite Automata Over Strong Bimonoids. Information Sciences 180, 3497–3520 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ćirić, M., Ignjatović, J., Bogdanović, S.: Fuzzy Equivalence Relations and Their Equivalence Classes. Fuzzy Sets and Systems 158, 1295–1313 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ćirić, M., Ignjatović, J., Bogdanović, S.: Uniform fuzzy relations and fuzzy functions. Fuzzy Sets and Systems 160, 1054–1081 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ćirić, M., Ignjatović, J., Damljanović, N., Bašić, M.: Bisimulations for Fuzzy Automata. Fuzzy Sets and Systems 186, 100–139 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ćirić, M., Ignjatović, J., Jančić, I., Damljanović, N.: Computation of the Greatest Simulations and Bisimulations Between Fuzzy Automata. Fuzzy Sets and Systems 208, 22–42

    Google Scholar 

  7. Ćirić, M., Stamenković, A., Ignjatović, J., Petković, T.: Fuzzy Relation Equations and Reduction of Fuzzy Automata. Journal of Computer and Systems Sciences 76, 609–633 (2010)

    Article  MATH  Google Scholar 

  8. Droste, M., Kuich, W., Vogler, H. (eds.): Handbook of Weighted Automata, Monographs in Theoretical Computer Science. EATCS Series. Springer (2009)

    Google Scholar 

  9. Ignjatović, J., Ćirić, M.: Weakly Linear Systems of Fuzzy Relation Inequalities and Their Applications: A Brief Survey. Filomat 26(2), 1–35 (2012)

    Google Scholar 

  10. Ignjatović, J., Ćirić, M., Bogdanović, S.: Determinization of Fuzzy Automata With Membership Values in Complete Residuated Lattices. Information Sciences 178, 164–180 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ignjatović, J., Ćirić, M., Bogdanović, S.: Fuzzy Homomorphisms of Algebras. Fuzzy Sets and Systems 160, 2345–2365 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ignjatović, J., Ćirić, M., Bogdanović, S.: On the Greatest Solutions to Weakly Linear Systems of Fuzzy Relation Inequalities and Equations. Fuzzy Sets and Systems 161, 3081–3113 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ignjatović, J., Ćirić, M., Bogdanović, S., Petković, T.: Myhill-Nerode Type Theory for Fuzzy Languages and Automata. Fuzzy Sets and Systems 161, 1288–1324 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Ignjatović, J., Ćirić, M., Damljanović, N., Jančić, I.: Weakly Linear Systems of Fuzzy Relation Inequalities: The Heterogeneous Case. Fuzzy Sets and Systems (2011), doi:10.1016/j.fss.2011.11.011

    Google Scholar 

  15. Ignjatović, J., Ćirić, M., De Baets, B.: General Method for Solving Equations and Inequalities Defined by Residuated Functions (to appear)

    Google Scholar 

  16. Ignjatović, J., Ćirić, M., Simović, V.: Fuzzy Relation Equations and Subsystems of Fuzzy Transition Systems. Knowledge-based Systems (2012), doi:10.1016/j.knosys.2012.02.008

    Google Scholar 

  17. Jančić, Z., Ignjatović, J., Ćirić, M.: An Improved Algorithm for Determinization of Weighted and Fuzzy Automata. Information Sciences 181, 1358–1368 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lee, E.T.-Z., Zadeh, L.A.: Note on Fuzzy Languages. Information Sciences 1, 421–434 (1969)

    Article  MathSciNet  Google Scholar 

  19. Li, Y., Pedrycz, W.: Fuzzy Finite Automata and Fuzzy Regular Expressions With Membership Values in Lattice Ordered Monoids. Fuzzy Sets and Systems 156, 68–92 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  20. Peeva, K.: Behaviour, Reduction and Minimization of Finite L-automata. Fuzzy Sets and Systems 28, 171–181 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  21. Peeva, K.: Finite L-fuzzy Machines. Fuzzy Sets and Systems 141, 415–437 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  22. Peeva, K., Kyosev, Y.: Fuzzy Relational Calculus: Theory, Applications, and Software. World Scientific (2004)

    Google Scholar 

  23. Stamenković, A., Ćirić, M., Ignjatović, J.: Reduction of Fuzzy Automata by Means of Fuzzy Quasi-orders. Submitted to Information Sciences

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ćirić, M., Ignjatović, J. (2013). Fuzziness in Automata Theory: Why? How?. In: Seising, R., Trillas, E., Moraga, C., Termini, S. (eds) On Fuzziness. Studies in Fuzziness and Soft Computing, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35641-4_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-35641-4_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35640-7

  • Online ISBN: 978-3-642-35641-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics