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)
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.
| Style | # |
|---|---|
| MLA | G. Marimuthu, S. Chanthirababu. "On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices." International Journal of Neutrosophic Science, Vol. 23, No. 2, 2024 ,PP. 270-285 (Doi : https://doi.org/10.54216/IJNS.230222) |
| APA | G. Marimuthu, S. Chanthirababu. (2024). On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices. Journal of International Journal of Neutrosophic Science, 23 ( 2 ), 270-285 (Doi : https://doi.org/10.54216/IJNS.230222) |
| Chicago | G. Marimuthu, S. Chanthirababu. "On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices." Journal of International Journal of Neutrosophic Science, 23 no. 2 (2024): 270-285 (Doi : https://doi.org/10.54216/IJNS.230222) |
| Harvard | G. Marimuthu, S. Chanthirababu. (2024). On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices. Journal of International Journal of Neutrosophic Science, 23 ( 2 ), 270-285 (Doi : https://doi.org/10.54216/IJNS.230222) |
| Vancouver | G. Marimuthu, S. Chanthirababu. On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 2 ): 270-285 (Doi : https://doi.org/10.54216/IJNS.230222) |
| IEEE | G. Marimuthu, S. Chanthirababu, On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 2 , (2024) : 270-285 (Doi : https://doi.org/10.54216/IJNS.230222) |