Strong Admissible Reduction of Hesitant L-Fuzzy Automaton

[1] N. C. Basak, A. Gupta, On quotient machines of a fuzzy automata and the minimal machine, Fuzzy Sets and
Systems, 125(2) (2002), 223-229. https://doi.org/10.1016/S0165-0114(01)00064-1

[2] B. Bedregal, R. Reiser, H. Bustince, C. Lopez-Molina, V. Torra, Aggregation functions for typical hesitant fuzzy
elements and the action of automorphisms, Information Sciences, 255 (2014), 82-99. https://doi.org/10.1016/
j.ins.2013.08.024

[3] W. Cheng, Z. W. Mo, Minimization algorithm of fuzzy finite automata, Fuzzy Sets and Systems, 141 (2004), 439-448.
https://doi.org/10.1016/S0165-0114(02)00607-3

[4] A. Choubey, K. Ravi, Intuitionistic fuzzy automata and intuitionistic fuzzy regular expressions, Journal of Applied
Mathematics and Informatics, 27(1-2) (2009), 409-417.

[5] V. S. Costa, B. Bedregal, On typical hesitant fuzzy automata, Soft Computing, 24(12) (2020), 8725-8736. https:
//doi.org/10.1007/s00500-020-04896-7

[6] A. H. Dehmiry, M. Mashinchi, R. Mesiar, Hesitant L-fuzzy sets, International Journal of Intelligent Systems, 33
(2018), 1027-1042. https://doi.org/10.1002/int.21910

[7] J. R. Gonzalez de Mendivil, Conditions for minimal fuzzy deterministic finite automata via brzozowski’s procedure,
IEEE Transactions on Fuzzy Systems, 26 (2018), 2409-2420. https://doi.org/10.1109/TFUZZ.2017.2775601

[8] A. G. D. M. Grau, S. Stanimirovic, F. Farina, Minimal determinization algorithm for fuzzy automata, IEEE Transactions
on Fuzzy Systems, 31 (2023), 3812-3822. https://doi.org/10.1109/TFUZZ.2023.3268406

[9] S. Halamish, O. Kupferman, Minimizing deterministic lattice automata, ACM Transactions on Computational Logic,
6604 (2015), 199-213. https://doi.org/10.1007/978-3-642-19805-2_14

[10] J. Ignjatovic, M. Ciric, S. Bogdanovic, T. Petkovic, Myhill-Nerode type theory for fuzzy languages and automata,
Fuzzy Sets and Systems, 161 (2010), 1288-1324. https://doi.org/10.1016/j.fss.2009.06.007

[11] Z. Jancic, M. Ciric, Brzozowski type determinization for fuzzy automata, Fuzzy Sets and Systems, 249 (2014),
73-82. https://doi.org/10.1016/j.fss.2014.02.021

[12] Y. B. Jun, Quotient structures of intuitionistic fuzzy finite state machines, Information Sciences, 177 (2007),
4977-4986. https://doi.org/10.1016/j.ins.2007.06.008

[13] V. Ladimir, V. Topencharov, K. Peeva, Equivalence, reduction and minimization on finite fuzzy automata, Journal
of Mathematica Analysis and Applications, 84 (1981), 270-281. https://doi.org/10.1016/0022-247X(81)
90165-7

[14] H. S. Lee, Minimizing fuzzy finite automata, 2000. Fuzzy Systems, FUZZ IEEE 2000. The Ninth IEEE International
Conference on, 1 (2000), 65-70. https://doi.org/10.1109/FUZZY.2000.838635

[15] E. T. Lee, L. A. Zadeh, Note on fuzzy languages, Information Sciences, 1 (1969), 421-434. https://doi.org/10.
1016/0020-0255(69)90025-5

[16] Y. Li, W. Pedrycz, Minimization of lattice finite automata and its application to the decomposition of lattice
languages, Fuzzy Sets and Systems, 158 (2007), 1423-1436. https://doi.org/10.1016/j.fss.2007.03.003

[17] L. Li, D. Qiu. On the state minimization of fuzzy automata, IEEE Transactions on Fuzzy Systems, 23 (2015),
434-443. https://doi.org/10.1109/TFUZZ.2014.2315620

[18] A. Mateescu, A. Salomaa, K. Salomaa, S. Yu, Lexical analysis with a simple finite fuzzy automaton model, Journal
of Universal Computer Science, 1 (1995), 292-311. https://doi.org/10.1007/978-3-642-80350-5_28

[19] S. Moghari, M. M. Zahedi, Minimization of deterministic fuzzy tree automata, Journal of Fuzzy Set-Valued Analysis,
2014 (2014), 1-18. https://doi.org/10.5899/2014/jfsva-00191

[20] J. N. Mordeson, D. S. Malik, Fuzzy automata and languages theory and applications, Chapman Hall, CRC Boca
Raton, London, New York, Washington DC, 2002.

[21] D. Qiu, Supervisory control of fuzzy discrete event systems: A formal approach, IEEE Transactions on Systems,
Man and Cybernetics Part B, 35 (2005), 72-88. https://doi.org/10.1109/TSMCB.2004.840457

[22] K. Ravi, A. Choubey, Interval-valued fuzzy regular language, Journal of Applied Mathematics and Informatics,
28(3-4) (2010), 639-649.

[23] K. Ravi, A. Choubey, Myhill-Nerode theorem for interval-valued fuzzy regular language, In: AIP Conference
Proceedings. American Institute of Physics, Chandigarh, 1324(1) (2010), 30-33. https://doi.org/10.1063/1.
3526220

[24] M. Shamsizadeh, M. M. Zahedi, Intuitionistic general fuzzy automata, Soft Computing, 20 (2016), 3505-3519.
https://doi.org/10.1007/s00500-015-1969-x

[25] M. Shamsizadeh, M. M. Zahedi, Bisimulation of type 2 for BL-general fuzzy automata, Soft Computing, 23 (2019),
9843-9852. https://doi.org/10.1007/s00500-019-03812-y

[26] M. Shamsizadeh, M. M. Zahedi, On reduced fuzzy multiset finite automata, Soft Computing, 22 (2022), 13381-
13390. https://doi.org/10.1007/s00500-022-07549-z

[27] M. Shamsizadeh, M. M. Zahedi, Kh. Abolpour, Reduction of BL-general L-fuzzy automata, Iranian Journal of
Mathematical Sciences and Informatics, 18(1) (2023), 131-144. https://doi.org/10.52547/ijmsi.18.1.131

[28] M. Shamsizadeh, M. M. Zahedi, M. J. Agheli Goki, Minimization of hesitant L-fuzzy automata, Fuzzy Set and
System, 477 (2024), 108793. https://doi.org/10.1016/j.fss.2023.108793

[29] A. K. Srivastava, S. P. Tiwari, IF-topologies and IF-automata, Soft Computing, 14 (2010), 571-578. https://doi.
org/10.1007/s00500-009-0427-z

[30] S. P. Tiwari, Sh. Sharan, Fuzzy automata based on lattice-ordered monoid with algebraic and topological aspects,
Fuzzy Information and Engineering, 4 (2012), 155-164. https://doi.org/10.1007/s12543-012-0108-y

[31] S. P. Tiwari, A. K. Srivastava, On a decomposition of fuzzy automata, Fuzzy Sets and Systems, 151 (2005), 503-511.
https://doi.org/10.1016/j.fss.2004.06.014

[32] V. Torra, Hesitant fuzzy sets, International Journal of Intelligent Systems, 25 (2010), 529-539. https://doi.org/
10.1002/int.20418

[33] V. Torra, Y. Narukawa, On hesitant fuzzy sets and decision, 2009 IEEE International Conference on Fuzzy Systems.
IEEE, (2009), 1378-1382. https://doi.org/10.1109/FUZZY.2009.5276884

[34] A. Tripathi, R. Kaur, A review of state minimization and state reduction techniques in fuzzy automata, AIP
Conference Proceedings, 2061 (2019), 020-033. https://doi.org/10.1063/1.5086655

[35] W. G. Wee, On generalization of adaptive algorithm and application of the fuzzy sets concept to pattern classification,
Ph.D. Thesis, Purdue University, Lafayette, IN, 1967.

[36] L. Wu, D. Qiu, Automata theory based on complete residuated lattice-valued logic: Reduction and minimization,
Fuzzy Sets and Systems, 161 (2010), 1635-1656. https://doi.org/10.1016/j.fss.2009.12.011

[37] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965,) 338-353. https://doi.org/10.1016/S0019-9958(65)
90241-X