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International Journal of Neutrosophic Science
Volume 23 , Issue 2, PP: 286-295 , 2024 | Cite this article as | XML | Html |PDF

Title

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

  M. Anandhkumar 1 * ,   T. Harikrishnan 2 ,   S. M. Chithra 3 ,   V. Kamalakannan 4 ,   B. Kanimozhi 5

1  Department of Mathematics, IFET College of Engineering (Autonomous), Villupuram, Tamilnadu, India
    (anandhkumarmm@gmail.com)

2  Department of Mathematics, Faculty of Science and Humanities, SRM Institute of Science and Technology, Ramapuram, Tamilnadu, India
    (mokshihari2009@gmail.com)

3  Department of Mathematics, R.M.K College of Engineering and Technology, Chennai, Tamilnadu, India
    (chithra.sm@rmkcet.ac.in)

4  Department of Mathematics, Panimalar Engineering College, Chennai, Tamilnadu, India
    (vkamalakannan@panimalar.ac.in)

5  Department of Mathematics, Sri Manakula Vinayagar Engineering College (Autonomous), Madagadipet Puducherry, India
    (kanimozhimaths@smvec.ac.in)

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Doi   :   https://doi.org/10.54216/IJNS.230223

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

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−idempotent NFM; T−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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[11] Mitra, S.K., Bhimasankaram, P., Malik, S.B. (2010). Matrix partial orders, shorted operators and applications. World Scientific.

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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

 

 

 

 

 

 

Cite this Article as :
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MLA M. Anandhkumar , T. Harikrishnan, S. M. Chithra, V. Kamalakannan, B. Kanimozhi. "Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices." International Journal of Neutrosophic Science, Vol. 23, No. 2, 2024 ,PP. 286-295 (Doi   :  https://doi.org/10.54216/IJNS.230223)
APA M. Anandhkumar , T. Harikrishnan, S. M. Chithra, V. Kamalakannan, B. Kanimozhi. (2024). Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices. Journal of International Journal of Neutrosophic Science, 23 ( 2 ), 286-295 (Doi   :  https://doi.org/10.54216/IJNS.230223)
Chicago M. Anandhkumar , T. Harikrishnan, S. M. Chithra, V. Kamalakannan, B. Kanimozhi. "Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices." Journal of International Journal of Neutrosophic Science, 23 no. 2 (2024): 286-295 (Doi   :  https://doi.org/10.54216/IJNS.230223)
Harvard M. Anandhkumar , T. Harikrishnan, S. M. Chithra, V. Kamalakannan, B. Kanimozhi. (2024). Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices. Journal of International Journal of Neutrosophic Science, 23 ( 2 ), 286-295 (Doi   :  https://doi.org/10.54216/IJNS.230223)
Vancouver M. Anandhkumar , T. Harikrishnan, S. M. Chithra, V. Kamalakannan, B. Kanimozhi. Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 2 ): 286-295 (Doi   :  https://doi.org/10.54216/IJNS.230223)
IEEE M. Anandhkumar, T. Harikrishnan, S. M. Chithra, V. Kamalakannan, B. Kanimozhi, Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 2 , (2024) : 286-295 (Doi   :  https://doi.org/10.54216/IJNS.230223)
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