IT-2 Fuzzy Automata and IT-2 Fuzzy Languages

  • M. K. DubeyEmail author
  • Priyanka Pal
  • S. P. Tiwari
Conference paper
Part of the Trends in Mathematics book series (TM)


The objective of this work is to give certain determinization and algebraic studies for an interval type-2 (IT-2) fuzzy automaton and language. We introduce a deterministic IT-2 fuzzy automaton and prove that it is behavioural equivalent to an IT-2 fuzzy automaton. Also, for a given IT-2 fuzzy language, we give certain recipe for constructions of deterministic IT-2 fuzzy automata.


  1. 1.
    Bělohlávek, R.: Determinism and fuzzy automata. Information Sciences, 143, 205–209 (2002)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Ćirić, M., Ignjatović, J.: Fuzziness in automata theory: why? how?. Studies in Fuzziness and Soft Computing, 298, 109–114 (2013)CrossRefGoogle Scholar
  3. 3.
    Holcombe, W. M. L.: Algebraic Automata Theory. Cambridge University Press, (1987)Google Scholar
  4. 4.
    Ignjatović, J., Ćirić, M., Bogdanović, S.: Determinization of fuzzy automata with membership values in complete residuated lattices. Information Sciences, 178, 164–180 (2008)MathSciNetCrossRefGoogle Scholar
  5. 5.
    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)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Jiang, Y., Tang, Y.: An interval type-2 fuzzy model of computing with words. Information Sciences, 281, 418–442 (2014)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Jun, Y. B.: Intuitionistic fuzzy finite state machines. Journal of Applied Mathematics and Computing, 17, 109–120 (2005)MathSciNetCrossRefGoogle Scholar
  8. 8.
    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)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Mendel, J. M., John, R. I.: Type-2 fuzzy sets made Simple. IEEE Transaction on Fuzzy Systems, 10, 117–127 (2002)CrossRefGoogle Scholar
  10. 10.
    Mendel, J. M., John, R. I., Liu, F.: Interval Type-2 fuzzy logic Systems made Simple. IEEE Transaction on Fuzzy Systems, 14, 808–821 (2006)CrossRefGoogle Scholar
  11. 11.
    Mordeson, J. N., Malik, D. S.: Fuzzy Automata and Languages, Theory and Applications. Chapman and Hall/CRC. London/Boca Raton, (2000)Google Scholar
  12. 12.
    Santos, E. S.: Max-product machines. Journal of Mathematical Analysis and Applications, 37, 677–686 (1972)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Tiwari, S.P., Yadav, V. K., Singh, A.K.: Construction of a minimal realization and monoid for a fuzzy language: a categorical approach. Journal of Applied Mathematics and Computing, 47, 401–416 (2015)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Tiwari, S.P., Yadav, V. K., Singh, A. K.: On algebraic study of fuzzy automata. International Journal of Machine Learning and Cybernetics, 6, 479–485 (2015)CrossRefGoogle Scholar
  15. 15.
    Tiwari, S.P., Yadav, V. K., Dubey, M.K.: Minimal realization for fuzzy behaviour: A bicategory-theoretic approach. Journal of Intelligent & Fuzzy Systems, 30, 1057–1065 (2016)CrossRefGoogle Scholar
  16. 16.
    Tiwari, S.P., Gautam, V., Dubey, M.K.: On fuzzy multiset automata. Journal of Applied Mathematics and Computing, 51, 643–657 (2016)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Wee, W. G.: On generalizations of adaptive algorithm and application of the fuzzy sets concept to pattern classification. Ph. D. Thesis, Purdue University, Lafayette, IN, (1967)Google Scholar
  18. 18.
    Wee, W. G., Fu, K.S.: A formulation of fuzzy automata and its application as a model of learning systems. IEEE Transactions on Systems, Man and Cybernetics, 5, 215–223 (1969)zbMATHGoogle Scholar
  19. 19.
    Wu, D., Mendel, J. M.: Uncertainty measures for interval type-2 fuzzy Sets. Information Sciences, 177, 5378–5393 (2007)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Wu, L., Qiu, D.: Automata theory based on complete residuated lattice-valued logic: Reduction and minimization. Fuzzy Sets and Systems, 161, 1635–1656 (2010)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Zadeh, L. A.: The concept of a linguistic variable and its application to approximate reasoning -1. Information Sciences, 8, 199–249 (1975)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsIndian Institute of Technology (ISM)DhanbadIndia

Personalised recommendations