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The objective of this study is to establish the results of secondary k- column symmetric (CS) Neutrosophic fuzzy matrices. Methods and Findings: We have applied CS condition in neutrosophic environment to find the relation between s-k CS, s- CS, k- CS and CS.

The characterization of interval valued (IV) secondary k-range symmetric (RS) Neutrosophic fuzzy matrices have been examined in this study with an example. It is discussed how IV s-k RS, s-RS, IV k-RS, and IV RS matrices relate to one another. We establish the necessary and sufficient criteria for IV s-k RS Neutrosophic fuzzy matrices. The existence of several generalized inverses of a matrix in IV Neutrosophic fuzzy matrices.

We develop the concept of range symmetric Neutrosophic Fuzzy Matrix and Kernel symmetric Neutrosophic Fuzzy Matrix analogous to that of an EP –matrix in the complex field. First we present equivalent characterizations of a range symmetric matrix and then derive equivalent conditions for a Neutrosophic Fuzzy Matrix to be kernel symmetric matrix and study the relation between range symmetric and kernel symmetric Neutrosophic Fuzzy Matrices. The idea of Kernel and k-Kernel Symmetric (k-KS) Neutrosophic Fuzzy Matrices (NFM) are introduced with an example. We present some basic results of kernel symmetric matrices. We show that k-symmetric implies k-Kernel symmetric but the converse need not be true. The equivalent relations between kernel symmetric, k-kernel symmetric and Moore-Penrose inverse of NFM are explained with numerical results.