Journal of Neutrosophic and Fuzzy Systems

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https://doi.org/10.54216/JNFS

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Volume 7 , Issue 2 , PP: 24-29, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

On a Two-Fold Algebra Based on the Standard Fuzzy Number Theoretical System

Mohammad Abobala 1 *

  • 1 Tishreen University, Department of Mathematics, Latakia, Syria - (Mohammadabobala777@gmail.com)
  • Doi: https://doi.org/10.54216/JNFS.070202

    Received: May 18, 2023 Revised: September 19, 2023 Accepted: November 14, 2023
    Abstract

    This paper is dedicated to studying the algebraic structure generated from the fusion of two-fold algebras with the standard fuzzy number theoretical system, where the novel fuzzy algebraic structure will be defined with a well-defined binary operation, and then its substructures will be studied concerning the corresponding operation such as hyper/under ideals, and two-fold fuzzy homomorphisms. Also, many examples will be illustrated to clarify the validity of our work.

    Keywords :

    two-fold algebra , fuzzy number theoretical system , two-fold fuzzy algebra , two-fold fuzzy homomorphism.

    References

    [1] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 ( 1971), 512-517.

    [2] P. Sivaramakrishna Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl. 84 (1981), 264-269.

    [3] T. M. Anthony, H. Sherwood, A characterization of fuzzy subgroups, Fuzzy Sets and Systems 7 (1982), 297-305.

    [4] W. M.Wu, “Normal fuzzy subgroups,” Fuzzy Mathematics, vol.1, no. 1, pp. 21–30, 1981.

    [5] Palaniappan, N, Naganathan,S and Arjunan, K “ A study on Intuitionistic L-Fuzzy Subgroups”, Applied Mathematical Sciences, vol. 3 , 2009, no. 53 , 2619-2624.

    [6] P.K. Sharma , “( α , β ) – Cut of Intuitionistic fuzzy Groups” International Mathematical Forum ,Vol. 6, 2011 , no. 53 , 2605-2614.

    [7] Florentine Smarandache. "Neutrosophic Two-Fold Algebra", Plithogenic Logic and Computation, Vol.1, No.1 2024. PP.11-15.

    [8] Mohammad Abobala. "On The Foundations of Fuzzy Number Theory and Fuzzy Diophantine Equations." Galoitica: Journal of Mathematical Structures and Applications, Vol. 10, No. 1, 2023 ,PP. 17-25 (Doi   :  https://doi.org/10.54216/GJMSA.0100102).

     

    Cite This Article As :
    Abobala, Mohammad. On a Two-Fold Algebra Based on the Standard Fuzzy Number Theoretical System. Journal of Neutrosophic and Fuzzy Systems, vol. , no. , 2023, pp. 24-29. DOI: https://doi.org/10.54216/JNFS.070202
    Abobala, M. (2023). On a Two-Fold Algebra Based on the Standard Fuzzy Number Theoretical System. Journal of Neutrosophic and Fuzzy Systems, (), 24-29. DOI: https://doi.org/10.54216/JNFS.070202
    Abobala, Mohammad. On a Two-Fold Algebra Based on the Standard Fuzzy Number Theoretical System. Journal of Neutrosophic and Fuzzy Systems , no. (2023): 24-29. DOI: https://doi.org/10.54216/JNFS.070202
    Abobala, M. (2023) . On a Two-Fold Algebra Based on the Standard Fuzzy Number Theoretical System. Journal of Neutrosophic and Fuzzy Systems , () , 24-29 . DOI: https://doi.org/10.54216/JNFS.070202
    Abobala M. [2023]. On a Two-Fold Algebra Based on the Standard Fuzzy Number Theoretical System. Journal of Neutrosophic and Fuzzy Systems. (): 24-29. DOI: https://doi.org/10.54216/JNFS.070202
    Abobala, M. "On a Two-Fold Algebra Based on the Standard Fuzzy Number Theoretical System," Journal of Neutrosophic and Fuzzy Systems, vol. , no. , pp. 24-29, 2023. DOI: https://doi.org/10.54216/JNFS.070202