Interval Valued Secondary k-Range Symmetric Quadri Partitioned Neutrosophic Fuzzy Matrices with Decision Making

Abstract

The objective of this study is to establish the results concerning Interval-Valued (IV) Secondary 
k-Range Symmetric (RS) Quadri Partitioned Neutrosophic Fuzzy Matrices (QPNFM). We have applied 
the RS condition within the neutrosophic environment to explore the relationships between IVQP s−k- 
RS, s-RS, IVQP k-RS, and IVQP RS matrices. This analysis has yielded significant insights into how these 
various matrix types interrelate and their structural properties. We have established the necessary and 
sufficient criteria for IVQP s−k-RS IVQPNFM, along with various generalized inverses of an IVQP s−ks- 
RS fuzzy matrix to maintain its classification as an IVQP s−k- RS matrix. Furthermore, we have 
characterized the generalized inverses of an IVQP s−k- RS matrix S corresponding to the sets S = {1,2}, S = 
{1,2,3}, and S = {1, 2, 4}. This characterization contributes to the foundational understanding of 
generalized inverses in the context of IVQPNFM. Additionally, a graphical representation of RS, Column 
symmetric (CS), and kernel symmetric (KS) adjacency and incidence QPNFM is illustrated. It is shown 
that every adjacency QPNFM is symmetric, RS, CS, and KS, whereas the incidence matrix only satisfies 
KS conditions. Similarly, every RS adjacency QPNFM is a KS adjacency QPNFM, but a KS adjacency 
QPNFM does not necessarily imply RS QPNFM. In this paper, we present an application of soft graphs in decision-making through the use of the adjacency matrix of a soft graph. We have developed an 
algorithm for this purpose and provide an example to demonstrate its application. 

DOI: 10.5281/zenodo.14423663