Algebraic properties of Kernel symmetric neutrosophic fuzzy matrices

Abstract

We define secondary k-Kernel symmetric (KS) and provide numerical examples for neutrosophic fuzzy matrices (NFM). We discuss the relation between s-k- KS, sKS, k- KS and KS NFM. We identify the necessary and sufficient conditions for a NFM to be a s-k- KS NFM. We demonstrate that k-symmetry implies k-KS and the converse is true. Also, we illustrate a graphical representation of KS adjacency and incidence NFM. Every adjacency NFM is symmetric, kernel symmetric but incidence matrix satisfies only kernel symmetric conditions. We establish the existence of multiple generalized inverses of NFM in Fn and establish the additional equivalent conditions for certain g-inverses of a s-k-KS NFM to be s-k-KS. Also, we characterize the generalized inverses belonging to the sets ψ (1, 2), ψ (1, 2, 3) and ψ (1, 2, 4) of s-k- KS NFM ψ.