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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 23 , Issue 2 , PP: 286-295, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

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)

    • 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&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.

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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.

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    [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 :
    Anandhkumar, M.. , Harikrishnan, T.. , M., S.. , Kamalakannan, V.. , Kanimozhi, B.. Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices. International Journal of Neutrosophic Science, vol. , no. , 2024, pp. 286-295. DOI: https://doi.org/10.54216/IJNS.230223
    Anandhkumar, M. Harikrishnan, T. M., S. Kamalakannan, V. Kanimozhi, B. (2024). Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices. International Journal of Neutrosophic Science, (), 286-295. DOI: https://doi.org/10.54216/IJNS.230223
    Anandhkumar, M.. Harikrishnan, T.. M., S.. Kamalakannan, V.. Kanimozhi, B.. Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices. International Journal of Neutrosophic Science , no. (2024): 286-295. DOI: https://doi.org/10.54216/IJNS.230223
    Anandhkumar, M. , Harikrishnan, T. , M., S. , Kamalakannan, V. , Kanimozhi, B. (2024) . Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices. International Journal of Neutrosophic Science , () , 286-295 . DOI: https://doi.org/10.54216/IJNS.230223
    Anandhkumar M. , Harikrishnan T. , M. S. , Kamalakannan V. , Kanimozhi B. [2024]. Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices. International Journal of Neutrosophic Science. (): 286-295. DOI: https://doi.org/10.54216/IJNS.230223
    Anandhkumar, M. Harikrishnan, T. M., S. Kamalakannan, V. Kanimozhi, B. "Partial orderings, Characterizations and Generalization of k-idempotent Neutrosophic fuzzy matrices," International Journal of Neutrosophic Science, vol. , no. , pp. 286-295, 2024. DOI: https://doi.org/10.54216/IJNS.230223

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