Geodesic
Intuitionistic Fuzzy Monoids in an Intuitionistic Fuzzy Finite Automaton with Unique Membership Transition on an Input Symbol
Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 2, pp. 383-394.

Voir la notice de l'article provenant de la source Library of Science

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(𝒜) and S_𝒜 from an intuitionistic fuzzy transition function of the given IFAUM 𝒜. Also it is proved that F(𝒜) and S_𝒜 are anti-isomorphic as monoids.
Keywords: intuitionistic fuzzy monoid 
@article{DMGAA_2022_42_2_a9,
     author = {Jency Priya, K. and Rajaretnam, T.},
     title = {Intuitionistic {Fuzzy} {Monoids} in an {Intuitionistic} {Fuzzy} {Finite} {Automaton} with {Unique} {Membership} {Transition} on an {Input} {Symbol}},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {383--394},
     publisher = {mathdoc},
     volume = {42},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a9/}
}
TY  - JOUR
AU  - Jency Priya, K.
AU  - Rajaretnam, T.
TI  - Intuitionistic Fuzzy Monoids in an Intuitionistic Fuzzy Finite Automaton with Unique Membership Transition on an Input Symbol
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2022
SP  - 383
EP  - 394
VL  - 42
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a9/
LA  - en
ID  - DMGAA_2022_42_2_a9
ER  - 
%0 Journal Article
%A Jency Priya, K.
%A Rajaretnam, T.
%T Intuitionistic Fuzzy Monoids in an Intuitionistic Fuzzy Finite Automaton with Unique Membership Transition on an Input Symbol
%J Discussiones Mathematicae. General Algebra and Applications
%D 2022
%P 383-394
%V 42
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a9/
%G en
%F DMGAA_2022_42_2_a9
Jency Priya, K.; Rajaretnam, T. Intuitionistic Fuzzy Monoids in an Intuitionistic Fuzzy Finite Automaton with Unique Membership Transition on an Input Symbol. Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 2, pp. 383-394. http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a9/

[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