Volume 27 • Issue 2 • PP: 58-67 • 2026
The Integration of Symbolic 2-Plithogenic and Symbolic 3-Plithogenic Rational Functions
Open Access & Copyright
© 2026 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 primary aim of this study is to explore the integration of symbolic 2-plithogenic and 3 plithogenic rational functions by formulating explicit and simplified rules to facilitate their evaluation, by using the division symbolic 2-plithogenic and symbolic 3-plithogenic rational numbers respectively. In addition to the theoretical proof of these rules, relevant examples are provided to illustrate these ideas.
Keywords
References
[1] Khan, M. A., and Ali, R., “Advanced neutrosophic decision-making framework for multi-criteria problems,” Journal of Computational and Theoretical Nanoscience, vol. 22, no. 5, pp. 1105–1114, 2025.
[2] A. A. A. Agboola, “On refined neutrosophic algebraic structures”, Neutrosophic Sets and Systems, vol. 10, pp. 99-101, 2015.
[3] M. Abobala, “On some special elements in neutrosophic rings and refined neutrosophic rings”, Journal of New Theory, vol. 33, 2020.
[4] Abobala, M., “On Refined Neutrosophic Matrices and Their Applications In Refined Neutrosophic Al-gebraic Equations”, Journal Of Mathematics, Hindawi, 2021.
[5] Zhang, Y., Li, J., and Wang, X., “Neutrosophic analysis of uncertainty in decision-making processes,” Journal of Intelligent Fuzzy Systems, vol. 38, no. 2, pp. 1239–1249, 2020.
[6] Albasheer, O., Hajjari., A., and Dalla., R., “On The Symbolic 3-Plithogenic Rings and Their Algebraic Properties”, Neutrosophic Sets and Systems, Vol 54, 2023.
[7] Ali, R., and Hasan, Z., “An Introduction To The Symbolic 3-Plithogenic Vector Spaces”, Galoitica Journal Of Mathematical Structures and Applications, Vol. 6, 2023.
[8] Ali, R.; and Hasan, Z., “An Introduction to the Symbolic 3-Plithogenic Modules”, Galoitica Journal Of Mathematical Structures and Applications, Vol. 6, 2023.
[9] Alhasan, Y. A., Mohamed, M. E. A. M., Ahassan, Q., and Abdulfatah, R. A. “Division of 3-Refined Neutrosophic Numbers by using the Identification Method and the 3-Refined AH-Isometry”, Neutrosophic Sets and Systems, 80, 507-515, 2025.
[10] Alhasan, Y. A., Mohamed, M. E. A. M., Ahassan, Q., and Abdulfatah, R. A. “The Extended Study of the2-symbolic Plithogenic Numbers”,Plithogenic Log. Comp. Vol. 2 37–48, 2024.
[11] Basheer, O. A., Hajjari, A., and Dalla, R., “On the symbolic 3-plithogenic rings and their algebraic properties”, Neutrosophic Sets and Systems, 54(1), 5, 2023.
[12] Gupta, R., and Sharma, P., “A new approach to neutrosophic set theory and its applications in real-world problems,” of Applied Mathematics and Computation, vol. 405, p. 126302, 2021.
[13] Merkepci, H., “On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4- Plithogenic Real Square Matrices”, Symmetry, 2023.
[14] Musa, I. A., and Alhasan, Y. A., “The integral of 2-refined rational neutrosophic functions”, Neutrosophic Sets and Systems, 80(1), 40, 2025.
[15] Smarandache, F., “Introduction to the Symbolic Plithogenic Algebraic Structures (revisited)”, Neutrosophic Sets and Systems, vol. 53, 2023.
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.