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International Journal of Neutrosophic Science

Volume 21 , Issue 4 , PP: 155-159, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

The Geometrical Characterization for The Solutions of a Vectorial Equation By Using Weak Fuzzy Complex Numbers and Other Generalizations Of Real Numbers

Yaser Ahmad Alhasan 1 * , Lee Xu 2 , Raja Abdullah Abdulfatah 3 , Abuobida M. Ahmed Alfahal 4

  • 1 Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia - (y.alhasan@psau.edu.sa)
  • 2 University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China - (Leexu1244@yahoo.com)
  • 3 Deanship the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia - (r.abdulfatah@psau.edu.sa)
  • 4 Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia - (a.alfahal@psau.edu.sa.)

    • Doi: https://doi.org/10.54216/IJNS.210415

    Received: February 16, 2023 Revised: May 18, 2023 Accepted: August 02, 2023
    Abstract

    The main goal of this paper is to study the geometrical characterization of the solutions for a vectorial equation defined in the two/three dimensional Euclidean spaces. The geometrical characterization of the solutions for the desired vectorial equation is obtained for many different values of t based on the circles and spheres in some generalizations of the real field, especially dual numbers, weak fuzzy complex numbers split-complex numbers, and complex numbers.

    Keywords :

    A-curve , dual numbers , weak fuzzy complex numbers , split-complex numbers

    References

    [1] Deckelman, S.; Robson, B. Split-Complex Numbers and Dirac Bra-kets. Communications In Information and Systems 2014, 14, 135-159.

    [2] Akar, M.; Yuce, S.; Sahin, S. On The Dual Hyperbolic Numbers and The Complex Hyperbolic Numbers. Jcscm 2018, 8, DOI: 10.20967/jcscm.2018.01.001.

    [3] Smarandache, F., "Neutrosophic Set a Generalization of the Intuitionistic Fuzzy Sets", Inter. J. Pure Appl. Math., pp. 287-297. 2005.

    [4] Hatip, A., "An Introduction To Weak Fuzzy Complex Numbers ", Galoitica Journal Of Mathematical Structures and Applications, Vol.3, 2023.

    [5] Khaldi, A., " A Study On Split-Complex Vector Spaces", Neoma Journal Of Mathematics and Computer Science, 2023.

    [6] Merkepci, H., and Abobala, M., " On The Symbolic 2-Plithogenic Rings", International Journal of Neutrosophic Science, 2023.

    [7] Ahmad, K., " On Some Split-Complex Diophantine Equations", Neoma Journal Of Mathematics and Computer Science, 2023.

    [8] Ali, R., " On The Weak Fuzzy Complex Inner Products On Weak Fuzzy Complex Vector Spaces", Neoma Journal Of Mathematics and Computer Science, 2023.

    [9] Merkepci, M., and Abobala, M., " On Some Novel Results About Split-Complex Numbers, The Diagonalization Problem And Applications To Public Key Asymmetric Cryptography", Journal of Mathematics, Hindawi, 2023.

    [10] Albasheer, O., Hajjari., A., and Dalla., R., " On The Symbolic 3-Plithogenic Rings and TheirAlgebraic Properties", Neutrosophic Sets and Systems, Vol 54, 2023.

    [11] Abobala, M., On Refined Neutrosophic Matrices and Their Applications In Refined Neutrosophic Algebraic Equations, Journal Of Mathematics, Hindawi, 2021

    [12] Sarkis, M., "On The Solutions Of Fermat's Diophantine Equation In 3-refined Neutrosophic Ring of Integers", Neoma Journal of Mathematics and Computer Science, 2023.

    [13] Abobala, M., "On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations", Mathematical Problems in Engineering, Hindawi, 2021

    [14] Abobala, M., "A Study Of Nil Ideals and Kothe's Conjecture In Neutrosophic Rings", International Journal of Mathematics and Mathematical Sciences, hindawi, 2021.

    [15] Ali, R., and Hasan, Z., " An Introduction To The Symbolic 3-Plithogenic Modules ", Galoitica Journal Of Mathematical Structures and Applications, vol. 6, 2023.

    [16] Ali, R., and Hasan, Z., "An Introduction To The Symbolic 3-Plithogenic Vector Spaces", Galoitica Journal Of Mathematical Structures and Applications, vol. 6, 2023.

    [17] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings", Neutrosophic sets and systems, Vol. 45, 2021.

    Cite This Article As :
    Ahmad, Yaser. , Xu, Lee. , Abdullah, Raja. , M., Abuobida. The Geometrical Characterization for The Solutions of a Vectorial Equation By Using Weak Fuzzy Complex Numbers and Other Generalizations Of Real Numbers. International Journal of Neutrosophic Science, vol. , no. , 2023, pp. 155-159. DOI: https://doi.org/10.54216/IJNS.210415
    Ahmad, Y. Xu, L. Abdullah, R. M., A. (2023). The Geometrical Characterization for The Solutions of a Vectorial Equation By Using Weak Fuzzy Complex Numbers and Other Generalizations Of Real Numbers. International Journal of Neutrosophic Science, (), 155-159. DOI: https://doi.org/10.54216/IJNS.210415
    Ahmad, Yaser. Xu, Lee. Abdullah, Raja. M., Abuobida. The Geometrical Characterization for The Solutions of a Vectorial Equation By Using Weak Fuzzy Complex Numbers and Other Generalizations Of Real Numbers. International Journal of Neutrosophic Science , no. (2023): 155-159. DOI: https://doi.org/10.54216/IJNS.210415
    Ahmad, Y. , Xu, L. , Abdullah, R. , M., A. (2023) . The Geometrical Characterization for The Solutions of a Vectorial Equation By Using Weak Fuzzy Complex Numbers and Other Generalizations Of Real Numbers. International Journal of Neutrosophic Science , () , 155-159 . DOI: https://doi.org/10.54216/IJNS.210415
    Ahmad Y. , Xu L. , Abdullah R. , M. A. [2023]. The Geometrical Characterization for The Solutions of a Vectorial Equation By Using Weak Fuzzy Complex Numbers and Other Generalizations Of Real Numbers. International Journal of Neutrosophic Science. (): 155-159. DOI: https://doi.org/10.54216/IJNS.210415
    Ahmad, Y. Xu, L. Abdullah, R. M., A. "The Geometrical Characterization for The Solutions of a Vectorial Equation By Using Weak Fuzzy Complex Numbers and Other Generalizations Of Real Numbers," International Journal of Neutrosophic Science, vol. , no. , pp. 155-159, 2023. DOI: https://doi.org/10.54216/IJNS.210415

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