DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score: 0.4

SJR: 0.203

SNIP: 0.562

MCQ: 0.12

Index Copernicus: 121.02

Discussiones Mathematicae - General Algebra and Applications

Article in volume

Authors:

K. Jency Priya

K. Jency Priya

P.G. and Research Department of Mathematics
St. Joseph's College (Autonomous), Tiruchirappalli - 620 002
Tamilnadu, India

email: jencypriya9@gmail.com

T. Rajaretnam

T. Rajaretnam

P.G. and Research Department of Mathematics
St. Joseph's College (Autonomous), Tiruchirappalli - 620 002
Tamilnadu, India

email: t_rajaretnam@yahoo.com

Title:

Intuitionistic fuzzy monoids in an intuitionistic fuzzy finite automaton with unique membership transition on an input symbol

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications 42(2) (2022) 383-394

Received: 2020-05-19 , Revised: 2021-02-15 , Accepted: 2022-06-02 , Available online: 2022-10-05 , https://doi.org/10.7151/dmgaa.1397

Abstract:

An intuitionistic fuzzy finite state automaton assigns a membership and nonmembership values in which there is a unique membership transition on an input symbol (IFAUM) is considered.It is proved and illustrated the existence of two different intuitionistic fuzzy monoids $ F(\mathscr{A})$ and $S_\mathscr{A}$ from an intuitionistic fuzzy transition function of the given IFAUM $\mathscr{A}$. Also it is proved that $F(\mathscr{A})$ and $S_\mathscr{A}$ are anti-isomorphic as monoids.

Keywords:

intuitionistic fuzzy monoid

References:

  1. K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20 (1986) 87–96.
    https://doi.org/10.1016/S0165-0114(86)80034-3
  2. K.T. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets Syst. 33 (1989a) 37–46.
    https://doi.org/10.1016/0165-0114(89)90215-7
  3. K.T. Atanassov, Intuitionistic fuzzy relations, First Scientific Session of the Mathematical Foundation Artificial Intelligence (Sofia IM-MFAIS, 1989b) 1–3.
  4. K.T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets Syst. 61 (2) (1994) 137–142.
    https://doi.org/10.1016/0165-0114(94)90229-1
  5. K.T. Atanassov, Intuitionistic Fuzzy Sets Theory and Applications (Physica-Verlag, Heidelberg, 1999).
    https://doi.org/10.1007/978-3-7908-1870-3
  6. Y.B. Jun, Intuitionistic fuzzy finite state machines, J. Appl. Math. Comput. 17 (1–2) (2005) 109–120.
    https://doi.org/10.1007/BF02936044
  7. Y.B. Jun, Intuitionistic fuzzy finite switchboard state machines, J. Appl. Math. Comput. 20 (1–2) (2006) 315–325.
    https://doi.org/10.1007/BF02831941
  8. Y.B. Jun, Quotient structures of intuitionistic fuzzy finite state machines, Inform. Sci. 177 (22) (2007) 4977–4986.
    https://doi.org/10.1016/j.ins.2007.06.008
  9. E.T. Lee and L.A. Zadeh, Note on fuzzy languages, Inform. Sci. 1 (1969) 421–434.
    https://doi.org/10.1016/0020-0255(69)90025-5
  10. Y.M. Li and Z.K. Shi, Remarks on uninorm aggregation operators, Fuzzy Sets Syst. 114 (2000) 377–380.
    https://doi.org/10.1016/S0165-0114(98)00247-4
  11. Y.M Li and W. Pedryez, Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoid, Fuzzy Sets Syst. 156 (2005) 68–92.
    https://doi.org/10.1016/j.fss.2005.04.004
  12. D.S. Malik and J.N. Mordeson, Fuzzy automata and languages, theory and applications, CRC, 2002.
  13. J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Language and Computation (Addison-Wesley, 1979).
  14. T. Rajaretnam and A. Ayyaswamy, Fuzzy finite state automaton with unique membership transition on an input Symbol, J. Combin. Math. and Combin. Comput. 69 (2009) 151–164.
  15. S. Eilenburg, Automata, Languages and Machines, Vol. A, (Academic Press, New York, 1976) 17–18.
  16. E.S. Santos, Maximum automata, Inform. Control 12 (1968) 367–377.
    https://doi.org/10.1016/S0019-9958(68)90123-X
  17. M.K. Sen and G. Chowdhry, Local behaviour of fuzzy automata, J. Fuzzy Math. 9 (4) (2001).
  18. M.G. Thomason and P.N. Marinos, Deterministic acceptors of regular fuzzy languages, IEEE Trans. Syst. Man. Cybern. 4 (1974) 228–230.
    https://doi.org/10.1109/TSMC.1974.5409123
  19. W.G. Wee and K.S. Fu, A formulation of fuzzy automata and its application as a model of learning systems, IEEE Trans. Syst. Man Cybern. 5 (1969) 215–223.
    https://doi.org/10.1109/TSSC.1969.300263
  20. M.S. Ying, A formal model of computing with words, IEEE Trans. Fuzzy Syst. 10 (5) (2002) 640–652.
    https://doi.org/10.1109/TFUZZ.2002.803497
  21. L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965) 338–353.
    https://doi.org/10.1016/S0019-9958(65)90241-X
  22. L.A Zadeh, Fuzzy languages and their relation to human and machine intelligence, Electrn. Research Laboratory University California, Berkeley, CA, Technical Report ERL-M302, 1971.
  23. X. Zhang and Y. Li, Intuitionistic fuzzy recognizers and intuitionistic fuzzy finite automata, J. Soft Comput. 13 (2009) 611–616.
    https://doi.org/10.1007/s00500-008-0338-4
Close