International Journal of Neutrosophic Science

Journal DOI

https://doi.org/10.54216/IJNS

Submit Your Paper

2690-6805ISSN (Online) 2692-6148ISSN (Print)

Volume 26 , Issue 2 , PP: 11-19, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

New Class of Equivalence Classes of Neutrosophic Fuzzy Delta- Algebras

Azeez Lafta Jaber 1 , Hussein S ALallak 2 , Jaafer Hmood Eidi 3 , Shuker Khalil 4 *

  • 1 Department of Mathematics, College of Education, University of Sumer, Iraq - (azeezlafta@gmail.com)
  • 2 General Directorate of Curricula. moe. Iraq - (hus201ein@gmail.com)
  • 3 Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq - ( drjaffarmath@uomustansiriyah.edu.iq)
  • 4 Department of Mathematics, College of Science, University of Basrah, Basrah 61004, Iraq - (shuker.khalil@uobasrah.edu.iq)
  • Doi: https://doi.org/10.54216/IJNS.260202

    Received: December 17, 2024 Revised: February 02, 2025 Accepted: March 01, 2025
    Abstract

    This work analyzes neutrosophic fuzzification in algebra, applies novel classes of neutrosophic fuzzy () to algebra, and explores the ideas of ideal (), subalgebra (), δ-homomorphism, and ideal (), exploring some of their descriptions. We shall demonstrate a variety of applications, including the notations  and  on  /  is  of }. We will also investigate their equivalence classes, evaluate our findings in light of the unique ideas offered in this work, and investigate related characteristics.

    Keywords :

    Neutrosophic Fuzzy set , algebra , Neutrosphic fuzzy subalgebra , Equivalence Classes

    References

    [1] L. A. Zadeh, "Fuzzy sets," Information Control, vol. 8, pp. 338–353, 1965.​

    [2] K. T. Atanassov, "Intuitionistic fuzzy sets," Fuzzy Sets and Systems, vol. 20, pp. 87–96, 1986.​

    [3] F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability. American Research Press, 1999.​

    [4] H. Wang, F. Smarandache, Y. Q. Zhang, and R. Sunderraman, Interval Neutrosophic Sets and Logic: Theory and Applications in Computing. Hexis, 2005.​

    [5] Y. B. Jun, F. Smarandache, and H. Bordbar, "Neutrosophic N-structures applied to BCK/BCI-algebras," Informatica, vol. 8, no. 4, p. 128, 2017.​

    [6] M. Khan, S. Anis, F. Smarandache, and Y. B. Jun, "Neutrosophic N-structures and their applications in semigroups," Annals of Fuzzy Mathematics and Informatics, vol. 14, pp. 583–598, 2017.​

    [7] K. Damodharan, M. Vigneshwaran, and S. Mahmood, "Nδ*gα-continuous and irresolute functions in neutrosophic topological spaces," Neutrosophic Sets and Systems, vol. 38, no. 1, pp. 439–452, 2020.​

    [8] S. M. Khalil and A. N. Hassan, "The characterizations of δ-algebras with their ideals," in IOP Conference Series: Journal of Physics, vol. 1999, no. 1, p. 012108, 2021, doi:10.1088/1742-6596/1999/1/012108.​

    [9] A. L. Jaber and S. M. Khalil, "New category of equivalence classes of intuitionistic fuzzy δ-algebras with their applications," in Smart Innovation, Systems and Technologies, vol. 302, pp. 651–663, 2022.​

    [10] N. A. Abbas, S. Khalil, and M. Vigneshwaran, "The neutrosophic strongly open maps in neutrosophic bi-topological spaces," Journal of Interdisciplinary Mathematics, vol. 24, no. 3, pp. 667–675, 2021.​

    [11] A. A. Atshan and S. M. Khalil, "Neutrosophic RHO–ideal with complete neutrosophic RHO–ideal in RHO–algebras," Neutrosophic Sets and Systems, vol. 55, pp. 300–315, 2023.​

    [12] N. M. Ali Abbas and S. Khalil, "On new classes of neutrosophic continuous and contra mappings in neutrosophic topological spaces," International Journal of Nonlinear Analysis and Applications, vol. 12, no. 1, pp. 718–725, 2021.​

    [13] J. H. Eidi, F. S. Fadhel, and A. E. Kadhm, "Fixed-point theorems in fuzzy metric spaces," International Journal of Mathematics and Computer Science, vol. 17, no. 3, pp. 1287–1298, 2022.​

    [14] F. S. Fadhel, J. H. Eidi, and H. M. Wali, "Contraction mapping theorem in partial fuzzy metric spaces," Journal of Applied Science and Engineering, vol. 25, no. 2, pp. 353–360, 2022.​

    [15] S. Khalil, A. Hassan, H. Alaskar, W. Khan, and A. Hussain, "Fuzzy logical algebra and study of the effectiveness of medications for COVID-19," Mathematics, vol. 9, no. 22, pp. 28–38, 2021.​

    [16] S. Mahmood, "Decision making using new category of similarity measures and study their applications in medical diagnosis problems," Afrika Matematika, vol. 32, pp. 865–878, 2021, doi:10.1007/s13370-020-00866-2.​

    [17] S. Mahmood and A. N. Hassan, "New class of algebraic fuzzy systems using cubic soft sets with their applications," in IOP Conference Series: Materials Science and Engineering, vol. 928, no. 4, p. 042019, 2020, doi:10.1088/1757-899X/928/4/042019.​

    [18] M. A. Hasan, S. Khalil, and N. M. Ali Abbas, "Characteristics of the soft-(1/2)-gprw-closed sets in soft bi-topological spaces," in 2020 International Conference on Emerging Trends in Engineering and Technology (ICETET), 2020, pp. 103–108, doi:10.1109/ITELA50150.2020.9253110.​

    [19] S. Mahmood, E. Suleiman, and N. M. Ali Abbas, "New technique to generate permutation measurable spaces," in 2021 International Conference on Information Technology (ICIT), 2021, pp. 160–163, doi:10.1109/BICITS51482.2021.9509892.

    [20] S. Alsalem, A. F. Al Musawi, and E. Suleiman, "On permutation B-center and derived permutation B-algebras," in 2022 7th International Conference on Mathematics and Computers in Sciences and Industry (MCSI), Athens, Greece, 2022, pp. 46–50, doi:10.1109/MCSI55933.2022.00014.

    [21] S. Alsalem, A. F. Al Musawi, and E. Suleiman, "On maximal permutation BH—ideals of permutation BH—algebras," in 2022 7th International Conference on Mathematics and Computers in Sciences and Industry (MCSI), Athens, Greece, 2022, pp. 40–45, doi:10.1109/MCSI55933.2022.00013.

    [22] Y. B. Jun, H. S. Kim, and D. S. Yoo, "Intuitionistic fuzzy d-algebras," Scientiae Mathematicae Japonica, vol. e-2006, no. 19, pp. 1289–1297, 2006.

    Cite This Article As :
    Lafta, Azeez. , S, Hussein. , Hmood, Jaafer. , Khalil, Shuker. New Class of Equivalence Classes of Neutrosophic Fuzzy Delta- Algebras. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 11-19. DOI: https://doi.org/10.54216/IJNS.260202
    Lafta, A. S, H. Hmood, J. Khalil, S. (2025). New Class of Equivalence Classes of Neutrosophic Fuzzy Delta- Algebras. International Journal of Neutrosophic Science, (), 11-19. DOI: https://doi.org/10.54216/IJNS.260202
    Lafta, Azeez. S, Hussein. Hmood, Jaafer. Khalil, Shuker. New Class of Equivalence Classes of Neutrosophic Fuzzy Delta- Algebras. International Journal of Neutrosophic Science , no. (2025): 11-19. DOI: https://doi.org/10.54216/IJNS.260202
    Lafta, A. , S, H. , Hmood, J. , Khalil, S. (2025) . New Class of Equivalence Classes of Neutrosophic Fuzzy Delta- Algebras. International Journal of Neutrosophic Science , () , 11-19 . DOI: https://doi.org/10.54216/IJNS.260202
    Lafta A. , S H. , Hmood J. , Khalil S. [2025]. New Class of Equivalence Classes of Neutrosophic Fuzzy Delta- Algebras. International Journal of Neutrosophic Science. (): 11-19. DOI: https://doi.org/10.54216/IJNS.260202
    Lafta, A. S, H. Hmood, J. Khalil, S. "New Class of Equivalence Classes of Neutrosophic Fuzzy Delta- Algebras," International Journal of Neutrosophic Science, vol. , no. , pp. 11-19, 2025. DOI: https://doi.org/10.54216/IJNS.260202