Fuzzy Finite Switchboard Automata with Complete Residuated Lattices

  • Authors

    • Nur Ain Ebas
    • Nor Shamsidah Amir Hamzah
    • Kavikumar Jacob
    • Mohd Saifullah Rusiman
    2018-11-30
    https://doi.org/10.14419/ijet.v7i4.30.22099
  • Complete Residuated Lattices, Fuzzy Finite Automata, Fuzzy Finite Switchboard Automata, Switchboard Subsystems
  • The theory of fuzzy finite switchboard automata (FFSA) is introduced by the use of general algebraic structures such as complete residuated lattices in order to enhance the process ability of FFSA. We established the notion of homomorphism, strong homomorphism and reverse homomorphism and shows some of its properties. The subsystem of FFSA is studied and the set of switchboard subsystem-forms a complete  -sublattices is shown. The algorithm of FFSA with complete residuated lattices is given and an example is provided.

     

  • References

    1. [1] Pan H, Cao Y, Zhang M & Chen Y (2014), Simulation for lattice-valued doubly labeled transitions systems. International Journal of Approximate Reasoning 55, 797-811.

      [2] Konecny J & Krupka M (2017), Complete relations on fuzzy complete lattices. Fuzzy Sets and Systems 320, 64-80.

      [3] Sato Y & Kuroki N (2002), Fuzzy Finite Switchboard State Machine. The Journal of Fuzzy Mathematics 10, 863-873.

      [4] Ciric M, Ignjatovic J & Damljanovi’c N (2012), Bisimulations for fuzzy automata. Fuzzy Sets and Systems 186, 100-139.

      [5] Xing H, Qiu DW & Liu F (2009), Automata theory based on complete residuated lattice-valued logic: pushdown. Fuzzy Sets and Systems 160, 1125-1140.

      [6] Sato Y, Finite Switchboard State Machines and Fuzzy Finite Switchboard State Machines, Hyogo University of Teacher Education, (2003).

      [7] Rabin M & Scott D (1959), Finite Automata and Their Decision Problems. Ibm Journal of Research and Development 3, 114-125.

      [8] Mordeson JN & Malik DS, Fuzzy Automata and Languages, Theory and Applications, Chapman and Hall/CRC, London/Boca Raton, FL (2002).

      [9] Wu L, Qiu DW & Xing H (2012), Automata theory based on complete residuated lattice-valued logic: turing machines. Fuzzy Sets and Systems 208, 43-66.

      [10] Ignjatovic J, Ciric M & Simovic V (2013), Fuzzy relation equations and subsytems of fuzzy transition systems. Knowledge-Based Systems 38, 48-61.

      [11] Guo X (2012), A comment on “Automata theory based on complete residuated lattice-valued logic: Pushdown automataâ€. Fuzzy Sets and Systems 199, 130-135.

      [12] Tabak J, Algebra Sets, Symbols, and the Language of Thought, The History of Mathematics, Volume 1, Viva Books Private Limited, (2006).

      [13] Pan H, Li Y, Cao Y & Li P (2017), Nondeterministic fuzzy automata with membership values in complete residuated lattices, International Journal of Approximate Reasoning 82, 22-38.

      [14] Abolpour K & Zahedi MM (2017), General fuzzy automata based on complete residuated lattice-valued. Journal of Fuzzy Systems 14, 103-121.

      [15] Qiu DW (2001), Automata theory based on completed residuated lattice-valued logic(I), Science in China Series: Information Sciences 44, 419-429.

      [16] Dilworth RP (1938), Abstract residuation over lattices. Bulletin of the American Mathematical Society 44, 262-268.

      [17] Wu L & Qiu DW (2010), Automata theory based on complete residuated lattice-valued logic: reduction and minimization. Fuzzy Sets and Systems 161, 1635-1656.

      [18] Belohlavek R, Fuzzy Relational Systems: Foundations and Principles, Kluwer, (2002).

      [19] Ghorani M & Zahedi MM (2012), Characterizations of complete residuated lattice-valued finite tree automata. Fuzzy Sets and Systems 199, 28-46.

      [20] Qiu DW (2002), Automata theory based on completed residuated lattice- valued logic(II). Science in China Series:Information Sciences 45, 442-452.

      [21] Ciric M, Ignjatovic J & Pethovic T (2010), Fuzzy relation equation and reduction of fuzzy automata. Journal Computer System Science 76, 609 – 633.

      [22] Li Y (2011), Finite Automata Theory with Membership values in lattices. Information Sciences 181, 1003 – 1017.

      [23] Wee WG, On generalization of adaptive algorithm and application of the fuzzy sets concept

      [24] to pattern classification, Ph.D. Thesis, Purdue University, Lafayette, IN, (1967).

      [25] Li YM & Pedrycz W (2005), Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoids. Fuzzy Sets and Systems 156, 68–92.

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  • How to Cite

    Ebas, N. A., Hamzah, N. S. A., Jacob, K., & Rusiman, M. S. (2018). Fuzzy Finite Switchboard Automata with Complete Residuated Lattices. International Journal of Engineering & Technology, 7(4.30), 160-164. https://doi.org/10.14419/ijet.v7i4.30.22099