On Schur Complement in k-Kernel Symmetric Block Quadri  Partitioned Neutrosophic Fuzzy Matrices

K. Radhika; T. Harikrishnan; R. Ambrose Prabhu; P.Tharaniya; M.John peter; M.Anandhkumar

Authors

K. Radhika Department of Mathematics, Rajah Serfoji Government College (Autonomous) (Affiliated to Bharathidasan University), Thanjavur - 613005, Tamilnadu, India.
T. Harikrishnan Department of Mathematics, Faculty of Science and Humanities, SRM Institute of Science and Technology, Ramapuram, Tamilnadu, India
R. Ambrose Prabhu Department of Mathematics, Rajalakshmi Institute of Technology, Poonamalle, Chennai, Tamilnadu, India
P.Tharaniya Department of Mathematics, Rajalakshmi Institute of Technology, Poonamalle, Chennai, Tamilnadu, India
M.John peter Department of Mathematics, Panimalar Engineering College, Chennai – 600123, Tamil Nadu, India.
M.Anandhkumar Department of Mathematics, IFET College of Engineering (Autonomous), Villupuram, Tamilnadu, India.

Keywords:

QPNFM, Schur Complement, KS, k-KS

Abstract

In this paper, we present equivalent characterizations of k-kernel symmetric (k-KS)
Quadri Partitioned Neutrosophic Fuzzy Matrices (QPNFMs). Additionally, we establish the
necessary and sufficient conditions for the Schur complement (SC) within a k-KS QPNFM to be
k-symmetric. The study also offers equivalent characterizations of both KS and k-KS QPNFMs. A
few fundamental examples of KS QPNFMs are provided to clarify these concepts. It is shown that
although k-symmetry implies k-KS, the converse does not necessarily hold. Several fundamental
properties of k-KS QPNFMs are also derived. Finally, decision-making model utilizing QPNSMs has
been successfully developed and validated through its application to real-world problems.

DOI: 10.5281/zenodo.14271040