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
(kanigopi.a20@gmail.com)
6
Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco
(broumisaid78@gmail.com)
Abstract :
In this paper, we introduce the concept of reverse sharp ordering on Neutrosophic Fuzzy matrix (NFM) as a special case of minus ordering. We also introduce the concept of reverse left-T and right-T orderings for NFM as an analogue of left-star and right-star partial orderings for complex matrices. Several properties of these ordering are derived. We show that these ordering preserve its Moore-penrose inverse property. Finally, we show that these ordering are identical for certain class of NFM.
Keywords :
Neutrosophic fuzzy matrices; Reverse sharp ordering; Reverse left-T and right-T ordering; g-inverse; Moore-penrose inverses.
References :
[1] Atanassov, K., (1983), Intuitionistic Fuzzy Sets, Fuzzy Sets and System., 20, pp. 87- 96.
[2] Atanassov, K., (2005), Intuitionistic fuzzy implications and modus ponens, In Notes on Intuitionistic Fuzzy Sets., 11(1), pp. 1–5.
[3] Atanassov, K., (2005), On some types of fuzzy negations, In Notes on Intuitionistic Fuzzy Sets., 11(4), pp. 170–172.
[4] Jian Miao Chen., (1982), Fuzzy matrix partial orderings and generalized inverses, Fuzzy sets sys., 105, pp. 453 – 458.
[5] Meenakshi, AR., Inbam, C., (2004), The minus partial order in Fuzzy matrices, The Journal of Fuzzy matrices., 12 (3), pp. 695 - 700.
[6] Meenakshi, AR., (2008), Fuzzy matrix – Theory and its applications, MJP Publishers.
[7] Muthu Guru Packiam, K., Krishna Mohan, K.S., (2019), Partial orderings on k−idempotent fuzzy matrices., 15(5), pp. 733-741.
[8] Padder, R. A., Murugadas, P., (2022), Algorithm for controllable and nilpotent intuitionistic fuzzy matrices, Afr. Mat., 33(3), pp.84.
[9] Padder, R. A., Murugadas, P., (2019), Determinant theory for intuitionistic fuzzy matrices, Afr. Mat., 30, pp.943–955.
[10] Punithavalli, G., ( 2020), The Partial Orderings of m-Symmetric Fuzzy Matrices, International journal of Mathematics Trends and Technology., 66(4), pp.705-803.
[11] Punithavalli, G., Anandhkumar, M., (2022) , Partial Orderings On K−Idempotent Intuitionistic Fuzzy Matrices., 54(2), pp.2096-3246.
[12] Pradhan, R., Pal, M., (2014), The generalized inverse of Atanassov’s intuitionistic fuzzy matrices, International Journal of Computational Intelligence Systems., 7(6), pp.1083-1095.
[13] Shyamal, A. K., Pal, M., (2002), Distance between intuitionistic fuzzy matrices, V.U.J. Physical Sciences., 8, pp.81-91.
[14] Sriram, S., Murugadas, P., (2010), The Moore-Penrose Inverse of Intuitionistic Fuzzy Matrices Int. Journal of Math. Analysis., 4( 36), pp. 1779 – 1786.
[15] Thomson, M. G., (1977), Convergence of Power of a Fuzzy Matrix, Journal of Mathematical Analysis and Applications., 57, pp.476-480.
[16] Zadeh, L. A., (1965), Fuzzy Sets, Information and control., 8, pp.338-353.
[17] Smarandache F (2005) Neutrosophic set—a generalization of the intuitionistic fuzzy set. Int J Pure Appl Math 24(3):287–297
[18] Wang H, Smarandache F, Zhang YQ, Sunderraman R (2010) Single valued neutrosophic sets. Multispace Multistruct 4:410–413
[19] M. Anandhk umar, Pseudo Similarity of Neutrosophic Fuzzy matrices, International Journal of Neutrosophic Science, Vol. 20, No. 04, PP. 191-196, 2023
[20] M. Anandhkumar, On various Inverse of Neutrosophic Fuzzy Matrices, International Journal of Neutrosophic Science, Vol. 21, No. 02, PP. 20-31, 2023
Style | # |
---|---|
MLA | 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. 4, 2023 ,PP. 135-145 (Doi : https://doi.org/10.54216/IJNS.210413) |
APA | M. Anandhkumar , T. Harikrishnan, S. M. Chithra, V. Kamalakannan, B. Kanimozhi, Broumi Said. (2023). Reverse Sharp and Left-T Right-T Partial Ordering on Neutrosophic Fuzzy Matrices. Journal of International Journal of Neutrosophic Science, 21 ( 4 ), 135-145 (Doi : https://doi.org/10.54216/IJNS.210413) |
Chicago | 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." Journal of International Journal of Neutrosophic Science, 21 no. 4 (2023): 135-145 (Doi : https://doi.org/10.54216/IJNS.210413) |
Harvard | M. Anandhkumar , T. Harikrishnan, S. M. Chithra, V. Kamalakannan, B. Kanimozhi, Broumi Said. (2023). Reverse Sharp and Left-T Right-T Partial Ordering on Neutrosophic Fuzzy Matrices. Journal of International Journal of Neutrosophic Science, 21 ( 4 ), 135-145 (Doi : https://doi.org/10.54216/IJNS.210413) |
Vancouver | 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. Journal of International Journal of Neutrosophic Science, (2023); 21 ( 4 ): 135-145 (Doi : https://doi.org/10.54216/IJNS.210413) |
IEEE | 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, Journal of International Journal of Neutrosophic Science, Vol. 21 , No. 4 , (2023) : 135-145 (Doi : https://doi.org/10.54216/IJNS.210413) |