Volume 27 • Issue 2 • PP: 392-406 • 2026
A Conceptual Approach for Algebraic Structure of Multi-Neutrosophic BCI/BCK Algebras
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A multi-neutrosophic set is a collection in which each element has a vector of truth indeterminacy, and falsity membership degree, rather than a Neutrosophic set. These vectors may correspond to multiple criteria, perspectives, or layers of information. Multi-neutrosophic sets are a more adaptive strategy for handling ambiguity in complex systems because they broaden neutrosophic sets and allow for better modeling of uncertain information. In this study, we have proposed the fundamental structure of multi-neutrosophic BCI/BCK Algebra and extended it to the category of multi-neutrosophic BCI(BCK) algebras. Theoretical results are presented along with examples. This study advances algebraic structure to multi-neutrosophic set and provides novel directions for future research in non-classical logic.
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References
[1] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3):338–353.
[2] Atanassov, K. T. (1986). Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 20(1):87–96.
[3] Hossain, M. S., Rahman, M. M. (2022). Neutrosophic set theory and its applications in decision- making problems. Journal of Applied Mathematics and Computational Mechanics, 21(1), 15-26.
[4] Is´eki, K. (1966). An algebra related with a propositional calculus. Proceedings of the Japan Academy, 42(1), 26-29.
[5] Yasuyuki, I. M. A. I. (1966). On Axiom Systems of Propositional Calculi. XIV. Proceedings of the Japan Academy, 42(1), 19-22.
[6] Jun, Y. B., & Xin, X. L. (2001). Involutory and invertible fuzzy BCK-algebras. Fuzzy sets and systems, 117(3), 463-469.
[7] Jun, Y. B., & Xin, X. L. (2001). Fuzzy prime ideals and invertible fuzzy ideals in BCK-algebras. Fuzzy sets and systems, 117(3), 471-476.
[8] Jun, Y. B., & Kim, K. H. (2000). Intuitionistic fuzzy ideals of BCK-algebras. International journal of mathematics and mathematical sciences, 24(12), 839-849.
[9] Zhan, J., Hamidi, M., and Borumand Saeid, A. (2016). Extended Fuzzy BCK-Subalgebras. Iranian Journal of Fuzzy Systems, 13(4):125–144.
[10] Jana, C., Senapati, T., & Pal, M. (2016). (ϵ, ϵ ∨ q)-intuitionistic fuzzy BCI-subalgebras of a BCI- algebra. Journal of Intelligent & Fuzzy Systems, 31(1), 613-621.
[11] Agboola, A. A. A., Davvaz, B., et al. (2015). Introduction to neutrosophic bci/bck-algebras. International Journal of Mathematics and Mathematical Sciences, 2015.
[12] Jun, Y. B. (2017). Neutrosophic subalgebras of several types in BCK/BCI-algebras. Annals of Fuzzy Mathematics and Informatics. Volume 14, No. 1, (2017), pp. 75–86
[13] Ozturk, M. A. and Jun, Y. B. (2018). Neutrosophic ideals in BCK/BCI-algebras based on neutrosophic points. Journal of the International Mathematical Virtual Institute Vol. 8(2018), 1-17
[14] Khademan, S., Zahedi, M., Borzooei, R., and Jun, Y. (2019). Neutrosophic Hyper BCK- ideals. Neutrosophic Sets and Systems, 27:201-217.
[15] Alharthy, K., Alshahrani, A., Khan, M. (2023). Analyzing neutrosophic structures in decision-making frameworks: A review. Journal of Computational and Theoretical Nanoscience, 20(4), 1234-1245.
[16] Bhatia, S., Kumar, R. (2021). Advanced neutrosophic algebraic structures and their applications in optimization problems. International Journal of Computational Mathematics, 99(10), 987-1004.
[17] Ibrahim, M. and Agboola, A. A. A. (2020). Introduction to NeutroHyperGroups. Neutrosophic Sets and Systems, 38:15–32.
[18] Alsubie, A., Al-Masarwah, A., Jun, Y. B., and Ahmad, A. G. (2021). An approach to BMBJ- Neutrosophic Hyper-BCK-Ideals of Hyper-BCK-Algebras. Journal of Mathematics, 1–10.
[19] Alsubie, A. and Al-Masarwah, A. (2021). MBJ-Neutrosophic Hyper BCK Ideals in Hyper BCK- Algebras. AIMS Mathematics, 6(6): 6107–6121.
[20] Santhakumar, S., Sumathi, I. R., & Mahalakshmi, J. (2023). A Novel Approach to the Algebraic Structure of Neutrosophic SuperHyper Algebra. Neutrosophic Sets and Systems, 60(1), 39.
[21] Smarandache, F. (2022). Introduction to SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. Journal of Algebraic Hyperstructures and Logical Algebras, 3(2):17-24.
[22] Zhang, Y., Liu, X. (2024). Extensions of fuzzy algebraic structures: A comprehensive analysis. Journal of Mathematical Analysis and Applications, 510(2), 567-580.
[23] Smarandache, F. (2023a). New types of soft set “hypersoft set, indetermsoft set, indetermhypersoft set, and treesoft set”: An improved version. Neutrosophic Systems with Applications, 8:35–41.
[24] Smarandache, F. (2023). Introduction to the multi-neutrosophic Set. Neutrosophic Sets and Systems, 61, 89-99.
[25] Santhakumar, S., Sumathi, I. R., & Mahalakshmi, J. (2025). A note on Category of SuperHyper BCI- Algebra. International Journal of Neutrosophic Science (IJNS), 25(2).
[26] Fujita, Takaaki & Smarandache, Florentin. (2025). Some Types of HyperNeutrosophic Set (6): multi- neutrosophic Set and Refined Neutrosophic Set.
[27] Al-Tamimi, T. A., Al-Swidi, L. A., & Al-Obaidi, A. H. (2024). Partner Sets for Generalizations of multi-neutrosophic Sets. International Journal of Neutrosophic Science (IJNS), 24(1).
[28] Zenozain, E. A. M., Delgado, R. M. C., & Rischmoller, J. C. V. (2025). Sensory Marketing Analysis: Exploring Uncertainty and Contradiction in Consumer Decision-Making. A multi-neutrosophic Analysis with ARAS. Neutrosophic Sets and Systems, 84, 175-187.
[29] Arias, E. A. O., Vargas, J. L. C., S´anchez, J. A. F., & Estrada, S. M. D. (2025). multi-neutrosophic Analysis of Financial Statements as a Basis for Strategic Decision-Making in Uncertain Environments. Neutrosophic Sets and Systems, 82, 370-380.
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