International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 23 , Issue 2 , PP: 270-285, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices

G. Marimuthu 1 * , S. Chanthirababu 2

  • 1 Department of Mathematics, A.V.V.M. Sri Pushpam College (Affiliated to Bharathidasan University, Tiruchirappalli), Poondi, Thanjavur, 613503, Tamilnadu, India. - (drgmarimuthu@gmail.com)
  • 2 Department of Mathematics, A.V.V.M. Sri Pushpam College (Affiliated to Bharathidasan University, Tiruchirappalli), Poondi, Thanjavur, 613503, Tamilnadu, India. - (scbtr1@gmail.com)
  • Doi: https://doi.org/10.54216/IJNS.230222

    Received: June 21, 2023 Revised: September 22, 2023 Accepted: December 30, 2023
    Abstract

    The present study provides the necessary and sufficient criteria for the k-Kernel symmetry (KS) of a Schur complement (SC) in a k-KS Neutrosophic Fuzzy matrices (NFM) and Intuitionistic Fuzzy Matrices (IFM). Equivalent characterizations of KS and k-KS NFM and IFM are presented in this work. We provide a few fundamental examples about KS NFM and IFM. It is demonstrated that while k-symmetric implies k-KS, but the converse need not be true. A few fundamental characteristics of k-KS IFM and NFM are obtained.

    Keywords :

    NFM , IFM , Schur Complement, KS , k-KS.

    References

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    [4] A. R. Meenakshi, Fuzzy Matrix: Theory and Applications, MJP, Chennai, India, 2008.

    [5]  R. D. Hill and S. R. Waters, “On κ-real and κ-Hermitian matrices,” Linear Algebra and Its Applications, vol. 169, pp. 17–29, 1992.

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    Cite This Article As :
    Marimuthu, G.. , Chanthirababu, S.. On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices. International Journal of Neutrosophic Science, vol. , no. , 2024, pp. 270-285. DOI: https://doi.org/10.54216/IJNS.230222
    Marimuthu, G. Chanthirababu, S. (2024). On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices. International Journal of Neutrosophic Science, (), 270-285. DOI: https://doi.org/10.54216/IJNS.230222
    Marimuthu, G.. Chanthirababu, S.. On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices. International Journal of Neutrosophic Science , no. (2024): 270-285. DOI: https://doi.org/10.54216/IJNS.230222
    Marimuthu, G. , Chanthirababu, S. (2024) . On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices. International Journal of Neutrosophic Science , () , 270-285 . DOI: https://doi.org/10.54216/IJNS.230222
    Marimuthu G. , Chanthirababu S. [2024]. On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices. International Journal of Neutrosophic Science. (): 270-285. DOI: https://doi.org/10.54216/IJNS.230222
    Marimuthu, G. Chanthirababu, S. "On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices," International Journal of Neutrosophic Science, vol. , no. , pp. 270-285, 2024. DOI: https://doi.org/10.54216/IJNS.230222