International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 25 , Issue 2 , PP: 206-211, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

On Neutrosophic of BE-Algebra

Marrwa A. Salih 1 , Dunia A. Jarwan 2 , Majid M. Abed 3 *

  • 1 Department of Mathematics, College of Education for Pure Science, University of Tikrit, Tikrit, Iraq - (marrwaabdallah1984@tu.edu.iq)
  • 2 Department of Applied Mathematics, College of Science, University of Anbar, Anbar, Iraq - (dunia.alawi@uoanbar.edu.iq)
  • 3 Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq - (majid_math@uoanbar.edu.iq)
  • Doi: https://doi.org/10.54216/IJNS.250218

    Received: February 17, 2024 Revised: May 09, 2024 Accepted: August 18, 2024
    Abstract

    The BE-Algebra was presented by Kim in 2007. After that, several authors studied this type of logic concept in algebra. In this paper, we introduce more properties and remarks of BE-Algebra. Note that (A,*,1) is called BE-algebra if   a A, b, c A: collect a*a=1, a*1=1, 1*a=a and a*(b*c)=b*(a*c). In addition, a Neutrosophic BE-filter FI subset of the Neutrosophic BE-algebra is Neutrosophic BE-algebra AI is Neutrosophic BE-subalgebra AI.  Some new results and the criterion to determine some properties of BE-algebra and several relationships with another algebra namely Hibert algebras (H-algebra).

    Keywords :

    BE-algebra , Neutrosophic set , BE-filter , BE-subalgebra , Atom element

    References

    [1]          L.A. Zadeh,Fuzzy sets, Information and Control, vol 8, pp. 338–353.1965.

    [2]          F. Smarandache, Neutrosophic probability, set, and logic, American Research Press: Rehoboth, IL, USA, 1998.

    [3]          Jamiatun Nadwa Ismail et al. The Integrated Novel Framework: Linguistic Variables in Pythagorean Neutrosophic Set with DEMATEL for Enhanced Decision Support. Int. J. Neutrosophic Sci., vol. 21, no. 2, pp. 129-141, 2023.

    [4]          Abed, M. M., Al-Jumaili, A. F., Al-sharqi, F. G. Some mathematical structures in a topological group. Journal of Algebra and Applied Mathematics. 2018, 16(2), 99-117.

    [5]          Al-Sharqi, F. G., Abed, M. M., & Mhassin, A. A. (2018). On polish groups and their applications. Journal of Engineering and Applied Sciences, 13(18), 7533-7536.

    [6]          Al-Omeri, W., & Jafari, S. (2018). On generalized closed sets and generalized pre-closed sets in neutrosophic topological spaces. Mathematics, 7(1), 1.

    [7]          Al-Sharqi, F., & Al-Quran, A. (2022). Similarity measures on interval-complex neutrosophic soft sets with applications to decision-making and medical diagnosis under uncertainty. Neutrosophic Sets and Systems, 51, 495-515.

    [8]          Abed, M. M. (2022). On Indeterminacy (Neutrosophic) of Hollow Modules. Iraqi Journal of Science, 2650-2655.

    [9]          F. Al-Sharqi, Y. Al-Qudah and N. Alotaibi, Decision-making techniques based on similarity measures of possibility neutrosophic soft expert sets. Neutrosophic Sets and Systems, 55(1) (2023), 358-382.

    [10]       F. Al-Sharqi, A. Ahmad, A. Al-Quran, Fuzzy parameterized-interval complex neutrosophic soft sets and their applications under uncertainty, J. Intell. Fuzzy Syst. 44,  (2023), 1453–1477.

    [11]       F. Al-Sharqi, A. Al-Quran, M. U. Romdhini, Decision-making techniques based on similarity measures of possibility interval fuzzy soft environment, Iraqi Journal for Computer Science and Mathematics, vol. 4, pp.18–29, 2023.

    [12]       Talak, A. F., & Abed, M. M. (2022, January). Injective module and C1-module. In AIP Conference Proceedings (Vol. 2386, No. 1). AIP Publishing.

    [13]       Agboola, A. A. A. (2015). On refined neutrosophic algebraic structures. Neutrosophic sets and systems, 10, 99-101

    [14]       Al-Quran, A., Al-Sharqi, F., Rodzi, Z. M., Aladil, M., Romdhini, M. U., Tahat, M. K., & Solaiman, O. S. (2023). The Algebraic Structures of Q-Complex Neutrosophic Soft Sets Associated with Groups and Subgroups. International Journal of Neutrosophic Science, 22(1), 60-77.

    [15]       M U Romdhini, a Al-Quran, F Al-Sharqi, M K Tahat, and A Lutfi. Exploring the Algebraic Structures of Q-Complex Neutrosophic Soft Fields. International Journal of Neutrosophic Science, 22(04):93–105, 2023.

    [16]       M U Romdhini, F Al-Sharqi, a Nawawi, A Al-Quran, and H Rashmanlou. Signless Laplacian energy of interval-valued fuzzy graph and its applications. Sains Malaysiana, 52(7):2127–2137, 2023.

    [17]       Zail, S. H., Abed, M. M., & Faisal, A. S. (2022). Neutrosophic BCK-algebra and Ω-BCK-algebra. International Journal of Neutrosophic Science, 19(3), 8-15.

    [18]       Jun, Y. B., Smarandache, F., & Bordbar, H. (2017). Neutrosophic 𝒩-structures applied to BCK/BCI-algebras. Information, 8(4), 128.‏‏

    [19]       F. Al-Sharqi, A. Al-Quran and Z. M. Rodzi, Multi-Attribute Group Decision-Making Based on Aggregation Operator and Score Function of Bipolar Neutrosophic Hypersoft Environment, Neutrosophic Sets and Systems, 61(1), 465-492, 2023.

    [20]       A. Al-Quran, F. Al-Sharqi, A. U. Rahman and Z. M. Rodzi, The q-rung orthopair fuzzy-valued neutrosophic sets: Axiomatic properties, aggregation operators and applications. AIMS Mathematics, 9(2), 5038-5070, 2024.

    [21]       Talak, A. F., & Abed, M. M. (2021, February). P-(S. P) Submodules and C1 (Extending) Modules. In Journal of Physics: Conference Series (Vol. 1804, No. 1, p. 012083). IOP Publishing.

    [22]       Abed, M. M. (2020). A new view of closed-CS-module. Italian Journal of Pure and Applied Mathematics, 43, 65-72.

    [23]       Hammad, F. N., & Abed, M. M. (2021, March). New results of injective module with divisible property. In Journal of Physics: Conference Series (Vol. 1818, No. 1, p. 012168). IOP Publishing.

    [24]       Kareem, F. F., & Abed, M. M. (2021, May). Generalizations of Fuzzy k-ideals in a KU-algebra with Semigroup. In Journal of Physics: Conference Series (Vol. 1879, No. 2, p. 022108). IOP Publishing.

    [25]       Z. bin M. Rodzi et al., “Integrated Single-Valued Neutrosophic Normalized Weighted Bonferroni Mean (SVNNWBM)-DEMATEL for Analyzing the Key Barriers to Halal Certification Adoption in Malaysia,” Int. J. Neutrosophic Sci., vol. 21, no. 3, pp. 106–114, 2023.

    [26]       Abdallah, M.., Alawi, D.. , Mohammed, M.. N-Refined Indeterminacy of Some Modules. Journal of International Journal of Neutrosophic Science, vol. 20, no. 2, 2023, pp. 20-26.

    [27]       K. Iseki, S. Tanaka, An introduction to theory of BCK-algebras, Math. Japon. 23 (1978), 1-26.

    [28]        H. S. Kim, Y. H. Kim, On BE-algebras, Sci. Math. Jpn. 66 (2007), 113-116.

    [29]       S. S. Ahn, K.S. So, on ideals and upper sets in BE-algebras, Sci. Math. Jpn. 68 (2008), 279-285.

    [30]       A. Walendziak, on implicative BE-algebras, Ann. Uni. Mar. Cur-Sklod. Sect, A, 76 (2022), 45-54.

    [31]       Z. Cilogu, Y. Ceven, Commutative and bounded BE-algebras, Algebra, 2013 (2013), 1-6.

    [32]        L. C. Ciungu, Commutative pseudo BE-algebras, Iran. J. Fuzzy Syst., 13 (2016), 131-144.

    [33]       N. Olgan and A. Khatib, "Neutrosophic Modules," Journal of Biometric Applications. Vol. 3, No.2, 2018.

    Cite This Article As :
    A., Marrwa. , A., Dunia. , M., Majid. On Neutrosophic of BE-Algebra. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 206-211. DOI: https://doi.org/10.54216/IJNS.250218
    A., M. A., D. M., M. (2025). On Neutrosophic of BE-Algebra. International Journal of Neutrosophic Science, (), 206-211. DOI: https://doi.org/10.54216/IJNS.250218
    A., Marrwa. A., Dunia. M., Majid. On Neutrosophic of BE-Algebra. International Journal of Neutrosophic Science , no. (2025): 206-211. DOI: https://doi.org/10.54216/IJNS.250218
    A., M. , A., D. , M., M. (2025) . On Neutrosophic of BE-Algebra. International Journal of Neutrosophic Science , () , 206-211 . DOI: https://doi.org/10.54216/IJNS.250218
    A. M. , A. D. , M. M. [2025]. On Neutrosophic of BE-Algebra. International Journal of Neutrosophic Science. (): 206-211. DOI: https://doi.org/10.54216/IJNS.250218
    A., M. A., D. M., M. "On Neutrosophic of BE-Algebra," International Journal of Neutrosophic Science, vol. , no. , pp. 206-211, 2025. DOI: https://doi.org/10.54216/IJNS.250218