Vector General Fuzzy Automaton: A Refining Analyzing

Main Article Content

M. Shamsizadeh, Kh. Abolpour, E. Movahednia, M. De la Sen


This study aims to investigate the refining relation between two vector general fuzzy automata (VGFA) and prove that refining relation is an equivalence relation. Moreover, Also, we prove that if there exists a refining equivalence between two VGFA, then they have the same language. After that, by considering the notion of refining equivalence, we present the quotient of VGFA. In particular, we show that any quotient of a given VGFA and the VGFA itself have the same language. Furthermore, using the quotient VGFA, we obtain a minimal VGFA with the same language.

Article Details


  1. Kh. Abolpour, M.M. Zahedi, M. Shamsizadeh, BL-General Fuzzy Automata and Minimal Realization: Based on the Associated Categories, Iran. J. Fuzzy Syst. 17 (2020), 155-169.
  2. N.C. Basak, A. Gupta, On Quotient Machines of a Fuzzy Automata and the Minimal Machine, Fuzzy Sets Syst. 125(2002), 223-229.
  3. W. Cheng, Z.W. Mo, Minimization Algorithm of Fuzzy Finite Automata, Fuzzy Sets Syst. 141 (2004), 439-448.
  4. P. Das, A Fuzzy Topology Associated With a Fuzzy Finite State Machine, Fuzzy Sets Syst. 105 (1999) 469-479.
  5. M. Doostfatemeh, S.C. Kremer, New Directions in Fuzzy Automata, Int. J. Approx. Reason. 38 (2005), 175-214.
  6. B.R. Gaines, L.J. Kohout, The Logic of Automata, Int. J. General Syst. 2 (1976), 191-208.
  7. M. Ghorani, S. Moghari, Decidability of the Minimization of Fuzzy Tree Automata With Membership Values in Complete Lattices, J. Appl. Math. Comput. 68 (2021), 461-478.
  8. A. Gonzalez de Mendívil Grau, S. Stanimirovic, F. Farina Figueredo, Minimal Determinization Algorithm for Fuzzy Automata, IEEE Trans. Fuzzy Syst. (2023), 1-10.
  9. J.H. Jin, Q.G. Li, Y.M. Li, Algebraic Properties of L-Fuzzy Finite Automata, Inf. Sci. 234 (2013), 182-202.
  10. Y.B. Jun, Quotient Structures of Intuitionistic Fuzzy Finite State Machines, Inf. Sci. 177 (2007), 4977-4986.
  11. Y.H. Kim, J.G. Kim, S.J. Cho, Products of T-Generalized State Machines and T-Generalized Transformation Semigroups, Fuzzy Sets Syst. 93 (1998), 87-97.
  12. E.T. Lee, L.A. Zadeh, Note on Fuzzy Languages, Inf. Sci. 1 (1969), 421-434.
  13. P. Li, Y.M. Li, Algebraic Properties of LA-Languages, Inf. Sci. 176 (2006), 3232-3255.
  14. Y.M. Li, A Categorical Approach to Lattice-Valued Fuzzy Automata, Fuzzy Sets Syst. 157 (2006), 855-864.
  15. Y. Li, J. Wei, Possibilistic Fuzzy Linear Temporal Logic and Its Model Checking, IEEE Trans. Fuzzy Syst. 29 (2021) 1899-1913.
  16. A. Mateescu, A. Salomaa, K. Salomaa, S. Yu, Lexical Analysis with a Simple Finite-Fuzzy-Automaton Model, in: H. Maurer, C. Calude, A. Salomaa (Eds.), J.UCS The Journal of Universal Computer Science, Springer Berlin Heidelberg, Berlin, Heidelberg, 1996: pp. 292–311.
  17. J. Mockor, A Category of Fuzzy Automata, Int. J. General Syst. 20 (1991), 73-82.
  18. J. Mockor, Fuzzy and Non-Deterministic Automata, Soft Comput. 3 (1999), 221-226.
  19. J. Mockor, Semigroup Homomorphisms and Fuzzy Automata, Soft Comput. 6 (2002), 422-427.
  20. D. Qiu, Automata Theory Based on Complete Residuated Lattice-Valued Logic, Sci. China Ser. F. 44 (2001), 419-429.
  21. D. Qiu, Automata Theory Based on Complete Residuated Lattice-Valued Logic (II). Sci. China Ser. F. 45 (2002), 442–452.
  22. D. Qiu, Automata Theory Based on Quantum Logic: Some Characterizations, Inf. Comput. 190 (2004), 179-195.
  23. D. Qiu, Characterizations of Fuzzy Finite Automata, Fuzzy Sets Syst. 141 (2004), 391-414.
  24. D. Qiu, Supervisory Control of Fuzzy Discrete Event Systems: A Formal Approach, IEEE Trans. Syst. Man Cybern. 35 (2005), 72-88.
  25. E. Raisi Sarbizhan, M. Mehdi Zahedi, M. Shamsizadeh, L-Graph Automata And Some Applications, Comput. J. 66 (2022), 1698-1716.
  26. G. G. Rigatos, Fault Detection and Isolation Based on Fuzzy Automata, Inf. Sci. 179 (2009), 1893-1902.
  27. E.S. Santos, Maximin Automata, Inf. Control. 12(1968), 367-377.
  28. E.S. Santos, On Reduction of Max-Min Machines, J. Math. Anal. Appl. 37 (1972), 677-686.
  29. M. Shamsizadeh, E. Movahednia, M. De la Sen, Isomorphism Between Two Vector General Fuzzy Automata, Informatica. (2023) 1-17.
  30. M. Shamsizadeh, M.M. Zahedi, Bisimulation of Type 2 for BL-General Fuzzy Automata, Soft Comput. 23 (2019), 9843-9852.
  31. M. Shamsizadeh, M.M. Zahedi, On Reduced Fuzzy Multiset Finite Automata, Soft Comput. 26 (2022), 13381- 13390.
  32. M. Shamsizadeh, M.M. Zahedi, Kh. Abolpour, Irreducible Fuzzy Multiset Finite Automaton, Comput. J. (2023), bxac193.
  33. M. Shamsizadeh, M.M. Zahedi, M. Golmohamadian, Kh. Abolpour, Zero-Forcing Finite Automata, Int. J. Ind. Math. 13 (2021), IJIM-1493.
  34. M. Thomason G., P.N. Marinos, Deterministic Acceptors of Regular Fuzzy Languages, IEEE Trans. Syst., Man, Cybern. SMC-4 (1974), 228-230.
  35. W.G. Wee, On Generalizations of Adaptive Algorithm and Application of the Fuzzy Sets Concept to Pattern Classification, Ph.D. Dissertation, Purdue University, West Lafayette, 1967.
  36. L. Zadeh, Fuzzy Sets, Inf. Control. 8 (1965), 338-353.
  37. M.M. Zahedi, M. Horry, Kh. Abolpor, Bifuzzy (General) Topology on Max-Min General Fuzzy Automata, Adv. Fuzzy Math. 3 (2008), 51-68.