Algebraic Properties of Interval -Valued Quadri Partitioned  Neutrosophic Fuzzy Matrices and their Application in  Multi-Criteria Decision- Making Problem

P.Tharini; C. Devi Shyamala Mary; P.Tharaniya; S. Prathap; S. Ramkumar; G. Dhanavel

Authors

P.Tharini Department of Mathematics, PPG Institute of Technology, Coimbatore, Tamilnadu, India.
C. Devi Shyamala Mary PG & Research Department of Mathematics, St.Joseph’s College of Arts & Science (Autonomous), Cuddalore, Tamilnadu, India.
P.Tharaniya Department of Mathematics, Rajalakshmi Institute of Technology, Poonamalle, Chennai, Tamilnadu, India.
S. Prathap Department of Mathematics, Panimalar Engineering College, Chennai, Tamil Nadu, India.
S. Ramkumar Department of Mathematics, Paavai Engineering College (Autonomous), Namakkal-637 018, Tamilnadu, India.
G. Dhanavel Department of English, IFET College of Engineering, Villupuram, Tamilnadu, India.

Keywords:

Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices, range-symmetric Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices, kernel-symmetric Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices, Moore-Penrose inverse, Decision-making.

Abstract

In this study, we introduce two novel matrix concepts in the neutrosophic fuzzy domain:
range-symmetric Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices and kernel
symmetric Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices. These matrices are
defined analogously to EP-matrices within the complex domain. Initially, we establish fundamental
characterizations of range-symmetric matrices and then derive the necessary and sufficient
conditions under which an Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices
becomes kernel-symmetric . A detailed analysis follows to explore the relationship between range
symmetric
and kernel-symmetric Interval-Valued Quadri Partitioned Neutrosophic Fuzzy
Matrices. Additionally, we introduce the concepts of Kernel and k-Kernel Symmetric Interval-Valued
Quadri Partitioned Neutrosophic Fuzzy Matrices, providing illustrative examples to demonstrate
their application. Basic results for kernel-symmetric Interval-Valued Quadri Partitioned
Neutrosophic Fuzzy Matrices are derived, highlighting that while k-symmetric implies k- kernel symmetric in Interval-Valued Quadri Partitioned Neutrosophic Fuzzy Matrices, the converse does
not necessarily hold. We further discuss the connections between kernel-symmetric, k- kernel
symmetric and the Moore-Penrose inverse of Interval-Valued Quadri Partitioned Neutrosophic
Fuzzy Matrices, supported by numerical examples. The study culminates in an algorithm tailored
for solving multi-criteria decision-making problems using Interval-Valued Quadri Partitioned
Neutrosophic Fuzzy Matrices, validated through an illustrative example that demonstrates its
practical utility.