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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
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Volume 23Issue 2PP: 270-285 • 2024

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

G. Marimuthu 1* ,
S. Chanthirababu 1
1Department of Mathematics, A.V.V.M. Sri Pushpam College (Affiliated to Bharathidasan University, Tiruchirappalli), Poondi, Thanjavur, 613503, Tamilnadu, India.
* Corresponding Author.
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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

[1] Zadeh L.A., Fuzzy Sets, Information and control.,(1965),,8, pp. 338-353.

[2] K.Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag, 1999.

[3] K. H. Kim and F. W. Roush, “Generalized fuzzy matrices,” Fuzzy Sets and Systems, vol. 4, no. 3, pp. 293–315, 1980.

[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.

[6] T. S. Baskett and I. J. Katz, “Theorems on products of EPr matrices,” Linear Algebra and Its Applications, vol. 2, pp. 87–103, 1969.

[7] A. R. Meenakshi and S. Krishnamoorthy, “On κ-EP matrices,” Linear Algebra and Its Applications, vol. 269, pp. 219–232, 1998.

[8] Meenakshi AR and Krishnamoorthy S, On Schur complement in k-EP matrices, Indian J.Pure appl.math (2002) 1889-1902.

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Marimuthu, G., Chanthirababu, S.. "On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices." International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 2, 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, Volume 23(Issue 2), 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 Volume 23, no. Issue 2 (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, Volume 23(Issue 2), pp. 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. 2024;Volume 23(Issue 2):270-285. DOI: https://doi.org/10.54216/IJNS.230222
G. Marimuthu, S. Chanthirababu, "On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices," International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 2, pp. 270-285, 2024. DOI: https://doi.org/10.54216/IJNS.230222
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