Volume 23 • Issue 2 • PP: 270-285 • 2024
On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices
Open Access & Copyright
© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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
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.
Cite This Article
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.