International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2400 2020 2020 Department of Mathematics, IFET College of Engineering (Autonomous), Villupuram, Tamilnadu, India M. .. Department of Mathematics, Faculty of Science and Humanities, SRM Institute of Science and Technology, Ramapuram, Tamilnadu, India T. Harikrishnan Department of Mathematics, R.M.K College of Engineering and Technology, Chennai, Tamilnadu, India S. M. Chithra Department of Mathematics, Panimalar Engineering College, Chennai, Tamilnadu, India V. Kamalakannan Department of Mathematics, Sri Manakula Vinayagar Engineering College (Autonomous), Madagadipet Puducherry, India B. Kanimozhi In this article, First, we study the different orderings for k-idempotent Neutrosophic fuzzy matrices (NFM). With this idea, we also discover some properties for the k- Neutrosophic fuzzy matrices and demonstrate the connection between the generalized inverse and different orderings. We also go through some properties for the T-ordering, T- reverse ordering, minus, and space ordering in k-idempotent Neutrosophic fuzzy matrices using the g-inverses with numerical examples is given. Minus ordering is a partial ordering in the set of all regular fuzzy matrices. We have introduced ordering on k− idempotent fuzzy matrices and developed the theory of fuzzy matrix partial ordering. The minus ordering and k−space ordering are identical for k− idempotent matrices. Next, we introduce and study the concept of k–Idempotent Neutrosophic fuzzy matrix as a generalization of idempotent NFM via permutations. It is shown that a kidempotent NFM reduces to an idempotent NFM if and only if PK = KP. The Conditions for power symmetric NFM to be k-idempotent are derived and some related results are given. 2024 2024 286 295 10.54216/IJNS.230223 https://www.americaspg.com/articleinfo/21/show/2400