International Journal of Neutrosophic Science

Journal DOI

https://doi.org/10.54216/IJNS

Submit Your Paper

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

Volume 27 , Issue 2 , PP: 58-67, 2026 | Cite this article as | XML | Html | PDF | Full Length Article

The Integration of Symbolic 2-Plithogenic and Symbolic 3-Plithogenic Rational Functions

Jenan Shtayat 1 * , Wael Mahmoud Mohammad Salameh 2 , Ahmad A. Abubaker 3 , Esraa Aljubarah 4 , Ahmed Atallah Alsaraireh 5 , S. Kalaiselvan 6

  • 1 Department of mathematics, Yarmouk University, Irbid 21163, Jordan - (Jenan@yu.edu.jo)
  • 2 Faculty of Information Technology, Abu Dhabi University, Abu Dhabi, United Arab Emirates - (wael.salameh@adu.ac.ae)
  • 3 Faculty of Computer Studies, Arab Open University, Saudi Arabia - (a.abubaker@arabou.edu.sa)
  • 4 Independent Researcher, Nabels, Palestine - (ea9136093@gmail.com)
  • 5 The university of Jordan–Aqaba Department of computer information systems, Jordan - (a.alsarairah@ju.edu.jo)
  • 6 Department of Mathematics, Bannari Amman Institute of Technology, Sathyamangalam-638401, Tamil Nadu, India - (priankalai@gmail.com)
  • Doi: https://doi.org/10.54216/IJNS.270206

    Received: February 07, 2025 Revised: May 25, 2025 Accepted: July 06, 2025
    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 :

    Symbolic 2-plithogenic rational functions , Symbolic 3-plithogenic rational functions , Division , Integral

    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 As :
    Shtayat, Jenan. , Mahmoud, Wael. , A., Ahmad. , Aljubarah, Esraa. , Atallah, Ahmed. , Kalaiselvan, S.. The Integration of Symbolic 2-Plithogenic and Symbolic 3-Plithogenic Rational Functions. International Journal of Neutrosophic Science, vol. , no. , 2026, pp. 58-67. DOI: https://doi.org/10.54216/IJNS.270206
    Shtayat, J. Mahmoud, W. A., A. Aljubarah, E. Atallah, A. Kalaiselvan, S. (2026). The Integration of Symbolic 2-Plithogenic and Symbolic 3-Plithogenic Rational Functions. International Journal of Neutrosophic Science, (), 58-67. DOI: https://doi.org/10.54216/IJNS.270206
    Shtayat, Jenan. Mahmoud, Wael. A., Ahmad. Aljubarah, Esraa. Atallah, Ahmed. Kalaiselvan, S.. The Integration of Symbolic 2-Plithogenic and Symbolic 3-Plithogenic Rational Functions. International Journal of Neutrosophic Science , no. (2026): 58-67. DOI: https://doi.org/10.54216/IJNS.270206
    Shtayat, J. , Mahmoud, W. , A., A. , Aljubarah, E. , Atallah, A. , Kalaiselvan, S. (2026) . The Integration of Symbolic 2-Plithogenic and Symbolic 3-Plithogenic Rational Functions. International Journal of Neutrosophic Science , () , 58-67 . DOI: https://doi.org/10.54216/IJNS.270206
    Shtayat J. , Mahmoud W. , A. A. , Aljubarah E. , Atallah A. , Kalaiselvan S. [2026]. The Integration of Symbolic 2-Plithogenic and Symbolic 3-Plithogenic Rational Functions. International Journal of Neutrosophic Science. (): 58-67. DOI: https://doi.org/10.54216/IJNS.270206
    Shtayat, J. Mahmoud, W. A., A. Aljubarah, E. Atallah, A. Kalaiselvan, S. "The Integration of Symbolic 2-Plithogenic and Symbolic 3-Plithogenic Rational Functions," International Journal of Neutrosophic Science, vol. , no. , pp. 58-67, 2026. DOI: https://doi.org/10.54216/IJNS.270206