Volume 23 , Issue 2 , PP: 270-285, 2024 | Cite this article as | XML | Html | PDF | Full Length Article
G. Marimuthu 1 * , S. Chanthirababu 2
Doi: https://doi.org/10.54216/IJNS.230222
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.
NFM , IFM , Schur Complement, KS , k-KS.
[1] Zadeh L.A., Fuzzy Sets, Information and control.,(1965),,8, pp. 338-353.
[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.
