Volume 25 • Issue 2 • PP: 206-211 • 2025
On Neutrosophic of BE-Algebra
Open Access & Copyright
© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
View PDF 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
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
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.