LB-valued General Fuzzy Automata and minimal Determinization

Document Type : Research Paper

Authors

1 Dept. of Math., Shiraz Branch, Islamic Azad University, Shiraz, Iran

2 [Automata, Fuzzy automata] Dept. of Math., Behbahan Khatam Alanbia University of Technology, Khouzestan, Iran

Abstract

Although a variety of methods have already been developed to convert and adapt a fuzzy automaton to its related language equivalent fuzzy deterministic finite automaton, they can still be applied merely for fuzzy automata which have been characterized over particular underlying sets of truth values. Filling this gap, thus, this study attempts to focus on developing a method for computing a minimal deterministic LB-valued general fuzzy automaton for an LB-valued GFA defined over a locally finite and divisible residuated lattice. This proposed method uses the concept of a reduction graph that helps us achieve a minimal deterministic LB-valued GFA. Accordingly, the present investigation aimed at establishing the notions related to L-valued language identified by LB-valued general fuzzy automata (LBvalued GFA) and also crisp deterministic LB-valued GFA ˜ Fc equivalent to LB-valued GFA ˜ F. It then indicated the properties of ˜ Fc. The method of determinization through factorization of L-valued states and also a method concerning state reduction were proposed and studied in details. In particular, the main focus and contribution of this study was the automaton H( ˜ Fc) which is recognized as a deterministic LB-valued GFA that assures the necessary conditions intended for minimality and that its size is always equal or lesser than a minimal crisp deterministic LB-valued GFA equivalent to that. The related concepts and the results obtained in this study have also been clarified and explicated
through representative examples.

Keywords

Main Subjects

References

[1] Kh. Abolpour, On LB-valued GFA: An LB-valued operator oriented view with t-norm/t-conorm and implicators,
New Mathematics and Natural Computation, 18(3) (2022), 573-592.
[2] Kh. Abolpour, A new characterization of congruence and the discrete Sugeno integral on LB-valued general fuzzy
automata, Fuzzy Sets and Systems, 460 (2023), 186-199.
[3] Kh. Abolpour, A. Broumand Saeid, Fundamental group of LB-valued general fuzzy automata, New Mathematics
and Natural Computation, 18(2) (2022), 545-558.
[4] Kh. Abolpour, M. M. Zahedi, New directions in LB-valued general fuzzy automata: A topological view, Filomat,
35(1) (2021), 251-270.
[5] Kh. Abolpour, M. M. Zahedi, LB-valued general fuzzy automata, Fuzzy Sets and Systems, 442 (2022), 288-308.
[6] G. Bailador, G. Trivino, Pattern recognition using temporal fuzzy automata, Fuzzy Sets and Systems, 161 (2010),
37-55.
[7] R. Belohlavek, Determinism and fuzzy automata, Information Sciences, 143 (2002), 205-209.
[8] R. Belohlavek, V. Vychodil, Fuzzy equational logic, studies in fuzziness and soft computing, Springer, Berlin-
Heidelberg, 2005.
[9] J. A. Brzozowski, Canonical regular expressions and minimal state graphs for de nite events, In Proc. Sympos.
Math. Theory of Automata (New York, 1962), Polytechnic Press of Polytechnic Inst. of Brooklyn, Brooklyn, N.Y.,
(1963), 529-561.
[10] M. Doostfatemeh, S. C. Kremer, New directions in fuzzy automata, International Journal of Approximate Reasoning,
38 (2005), 175-214.
[11] R. van Glabbeek, B. Ploeger, Five determinization algorithms, Conference: Implementation and Applications
of Automata, 13th International Conference, CIAA 2008, San Francisco, California, USA, July 21-24, (2008).
Proceedings. DOI: 10.1007/978-3-540-70844-5 17.
[12] J. R. Gonzalez de Mendivil, A generalization of Myhill-Nerode theorem, Fuzzy Sets and Systems, 301 (2016),
103-115.
[13] J. R. Gonzalez de Mendivil, J. R. Garitagoitia, Determinization of fuzzy automata via factorization of fuzzy states,
Information Sciences, 283 (2014), 165-179.
[14] J. E. Hopcroft, R. Motwani, J. D. Ullman, Introduction to automata theory, 3rd Edition. Addison-Wesley, 2007.
[15] J. Ignjatovic, M. Ciric, S. Bogdanovi, Determinization of fuzzy automata with membership values in complete
residuated lattices, Information Sciences, 178 (2008), 164-180.
[16] 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.
[17] Z. Jancic, J. Ignjatovic, M. Ciric, An improved algorithm for determinization of weighted and fuzzy automata,
Information Sciences, 181 (2011), 1358-1368.
[18] Z. Jancic, I. Micic, J. Ignjatovic, M. Ciric, Further improvement of determinization methods for fuzzy  nite au-
tomata, Fuzzy Sets and Systems, 301 (2015), 79-102.
[19] Y. M. Li, W. Pedrycz, Fuzzy  nite automata and fuzzy regular expressions with membership values in lattice ordered
monoids, Fuzzy Sets and Systems, 156 (2005), 68-92.
[20] Y. Li, J. Wei, Possibilistic fuzzy linear temporal logic and its model checking, IEEE Transactions on Fuzzy Systems,
29 (2021), 1899-1913.
[21] J. Mordeson, D. Malik, Fuzzy a utomata and languages: Theory and applications, Chapman and Hall, CRC Press,
London, Boca Raton, FL., 2002.
[22] D. Qiu, Automata theory based on quantum logic: Some characterizations, Information and Computation, 190
(2004), 179-195.
[23] D. Qiu, Characterizations of fuzzy  nite automata, Fuzzy Sets and Systems, 141 (2004), 391-414.
[24] D. Qiu, Automata theory based on quantum logic: Reversibilities and pushdown automata, Theoretical Computer
Science, 386 (2007), 38-56.
[25] G. G. Rigatos, Fault detection and isolation based on fuzzy automata, Information Sciences, 179(12) (2009), 1893-
1902.
[26] M. Shamsizadeh, M. M. Zahedi, Kh. Abolpour, Bisimulation for BL-general fuzzy automata, Iranian Journal of
Fuzzy Systems, 13 (2016), 35-50.
[27] M. Shamsizadeh, M. M. Zahedi, Kh. Abolpour, Admissible partition for Bl-general fuzzy automaton, Iranian Journal
of Fuzzy Systems, 15 (2018), 79-90.
[28] A. K. Srivastava, S. P. Tiwari, A topology for fuzzy automata, Lecture Notes in Arti cial Intelligence, 2275 (2002),
485-490.
[29] A. K. Srivastava, S. P. Tiwari, On relationships among fuzzy approximation operators, fuzzy topology, and fuzzy
automata, Fuzzy Sets and Systems, 138 (2003), 197-204.
[30] S. Stanimirovic, M. Ciric, J. Ignjatovic, Determinization of fuzzy automata by factorizations of fuzzy states and
right invariant fuzzy quasiorders, Information Sciences, 469(12) (2018), 79-100.
[31] S. P. Tiwari, S. Sharan, Fuzzy automata based on lattice-ordered monoids with algebraic and topological aspects,
Fuzzy Information and Engineering, 4 (2012), 155-164.
[32] S. P. Tiwari, S. Sharan, L-valued automata and associated topologies, International Journal of Granular Computing,
Rough Sets and Intelligent Systems, 3 (2013), 85-94.
[33] Q. Wu, Z. Han, Q. E. Wu, Application of fuzzy automata decisionmaking system in target control, Journal of
Computer and Communications, 5(10) (2017), 16-25.
Iranian Journal of Fuzzy Systems
Volume 21, Issue 1
January and February 2024
Pages 173-188

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