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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science
Full Length Article

Volume 23 • Issue 2 • PP: 286-295 • 2024

Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices

M. Anandhkumar 1*
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,
T. Harikrishnan 2
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,
S. M. Chithra 3
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,
V. Kamalakannan 4
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,
B. Kanimozhi 5
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1Department of Mathematics, IFET College of Engineering (Autonomous), Villupuram, Tamilnadu, India
2Department of Mathematics, Faculty of Science and Humanities, SRM Institute of Science and Technology, Ramapuram, Tamilnadu, India
3Department of Mathematics, R.M.K College of Engineering and Technology, Chennai, Tamilnadu, India
4Department of Mathematics, Panimalar Engineering College, Chennai, Tamilnadu, India
5Department of Mathematics, Sri Manakula Vinayagar Engineering College (Autonomous), Madagadipet Puducherry, India
* Corresponding Author.
DOI https://doi.org/10.54216/IJNS.230223
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: June 25, 2023 Revised: September 29, 2023 Accepted: December 27, 2023
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Abstract

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.

Keywords

k&minus idempotent NFM T&minus ordering minus ordering space ordering and inverses Idempotent NFM permutation IFM k-symmetric NFM.

References

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[6] M. Anandhkumar. V.Kamalakannan,S.M.Chitra, and Said Broumi, Pseudo Similarity of Neutrosophic Fuzzy matrices, International Journal of Neutrosophic Science, Vol. 20, No. 04, PP. 191-196, 2023 .

[7]M.Anandhkumar.B.Kanimozhi,V.Kamalakannan,S.M.Chitra, and Said Broumi, On various Inverse of Neutrosophic Fuzzy Matrices, International Journal of Neutrosophic Science, Vol. 21, No. 02, PP. 20-31, 2023.

[8] M. Anandhkumar ,T. Harikrishnan, S. M. Chithra , V. Kamalakannan , B. Kanimozhi , Broumi Said ,Reverse Sharp and Left-T Right-T Partial Ordering on Neutrosophic Fuzzy Matrices, International Journal of Neutrosophic Science, Vol. 21, No. 04, PP. 135-145, 2023.

[9] M.G. Thomason, Convergence of posets of a fuzzy matrix , Journal of Mathl.Anal. Appl., 57 (1977), 3 - 15.

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[13] K. Muthugurupackiam and K.S.Krishnamohan, Generalisation of Idempotent fuzzy matrices, International Journal of Applied Engineering Research, 13(13) (2018), 11087–11090.

[14] K. Muthugurupackiam and K.S.Krishnamohan, Some inverses on Generalised idempotent fuzzy matrices, Journal of Applied Science and Computations, 6(2), (2019), 249-254.

[15] K.Muthu Guru Packiam and K.S.Krishna Mohan Partial orderings on k−idempotent fuzzy matrices Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 15, Number 5 (2019), pp. 733-741.

[16]M.Anandhkumar; G.Punithavalli; T.Soupramanien; Said Broumi, Generalized Symmetric Neutrosophic Fuzzy Matrices, Neutrosophic Sets and Systems, Vol. 57,2023, 57, pp. 114–127.

[17] M.Anandhkumar, B.Kanimozhi, S.M. Chithra, V.Kamalakannan, .Reverse Tilde (T) and Minus Partial Ordering on Intuitionistic Fuzzy Matrices, Mathematical Modelling of Engineering Problems, 2023, 10(4), pp. 1427–1432

 

 

 

 

 

 

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Anandhkumar, M., Harikrishnan, T., Chithra, S. M., Kamalakannan, V., Kanimozhi, B.. "Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices." International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 2, 2024, pp. 286-295. DOI: https://doi.org/10.54216/IJNS.230223
Anandhkumar, M., Harikrishnan, T., Chithra, S., Kamalakannan, V., Kanimozhi, B. (2024). Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices. International Journal of Neutrosophic Science, Volume 23(Issue 2), 286-295. DOI: https://doi.org/10.54216/IJNS.230223
Anandhkumar, M., Harikrishnan, T., Chithra, S. M., Kamalakannan, V., Kanimozhi, B.. "Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices." International Journal of Neutrosophic Science Volume 23, no. Issue 2 (2024): 286-295. DOI: https://doi.org/10.54216/IJNS.230223
Anandhkumar, M., Harikrishnan, T., Chithra, S., Kamalakannan, V., Kanimozhi, B. (2024) 'Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices', International Journal of Neutrosophic Science, Volume 23(Issue 2), pp. 286-295. DOI: https://doi.org/10.54216/IJNS.230223
Anandhkumar M, Harikrishnan T, Chithra S, Kamalakannan V, Kanimozhi B. Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices. International Journal of Neutrosophic Science. 2024;Volume 23(Issue 2):286-295. DOI: https://doi.org/10.54216/IJNS.230223
M. Anandhkumar, T. Harikrishnan, S. Chithra, V. Kamalakannan, B. Kanimozhi, "Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices," International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 2, pp. 286-295, 2024. DOI: https://doi.org/10.54216/IJNS.230223
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