Interval valued kernel symmetric, k-kernel symmetric, range symmetric and column symmetric neutrosophic fuzzy matrices

Abstract

We present the range-symmetric, interval-valued neutrosophic fuzzy matrix (RS-IVNFM) and the kernel-symmetric, interval-valued neutrosophic fuzzy matrix (KSIVNFM), which are similar to the EP-matrices in the unitary domain. Additionally, we illustrate a graphical representation of KS, column-symmetric, and range-symmetric adjacency and incidence neutrosophic fuzzy matrices. Every adjacency NFM is symmetric, range-symmetric, column-symmetric, and kernel-symmetric, but the incidence matrix satisfies only the kernel-symmetric condition.Similarly, every range-symmetric adjacency NFM is a kernel-symmetric adjacency NFM, but a kernel-symmetric adjacency NFM need not be range-symmetric. We first present equivalent characterizations for an RS matrix. Then, we derive the equivalent condition for an IVNFM to be a KS matrix, and finally, we study the relationship between RS-IVNFM and KS-IVNFM. With suitable examples, we introduce the concept of k-KS and RS-IVNFM. We also present some primary results about KS matrices. We demonstrate that KS implies k-KS, but the Converse need not apply. Numerical results illustrate the equivalent relationships between KS, the Moore-Penrose inverse of IVNFM, and k-KS.