Volume 19 , Issue 1 , PP: 342-349, 2022 | Cite this article as | XML | Html | PDF | Full Length Article
Mohammad Abobala 1 * , M. Bisher Ziena 2 , R. Iqbal Doewes 3 , Zahraa Hussein 4
Doi: https://doi.org/10.54216/IJNS.190131
The aim of this paper is to solve the problem of representing refined neutrosophic matrices by linear functions, where it describes the structure of refined neutrosophic linear transformations that represent refined neutrosophic matrices. On the other hand, this work introduces a novel algorithm to compute a basis of any refined neutrosophic vector space depending on the classical basis of its corresponding classical vector space.
Refined neutrosophic space , refined neutrosophic matrix , Linear transformation.
[1] Abobala, M., On Refined Neutrosophic Matrices and Their Applications In Refined Neutrosophic Algebraic Equations, Journal Of Mathematics, Hindawi, 2021
[2] Abobala, M., On The Representation of Neutrosophic Matrices by Neutrosophic Linear Transformations, Journal of Mathematics, Hindawi, 2021.
[3] Abobala, M., Hatip, A., Bal,M.," A Study Of Some Neutrosophic Clean Rings", International journal of neutrosophic science, 2022.
[4] Abobala, M., Hatip, A., Olgun, N., Broumi, S., Salama, A,A., and Khaled, E, H., The Algebraic Creativity In The Neutrosophic Square Matrices, Neutrosophic Sets and Systems, Vol. 40, pp.1-11, 2021.
[5] Dhar M., Broumi S.,and Smarandache F., "A Note on Square Neutrosophic Fuzzy Matrices", Neutrosophic Sets and Systems'', Vol. 3, pp. 37-41 2014.
[6] Agboola, A.A.A., “On Reļ¬ned Neutrosophic Algebraic Structures”, Neutrosophic Sets and Systems,Vol.10, pp. 99-101, 2015.
[7] Das, R., Smarandache, F., and Tripathy, B., "Neutrosophic Fuzzy Matrices and Some Algebraic Operations", Neutrosophic Sets and Systems, Vol. 32, pp. 401-409, 2020
[8] W. B. Vasantha Kandasamy Florentin Smarandache K. Ilanthenral, INTRODUCTION TO BIMATRICES, HIXIS, 2005.
[9] Adeleke, E.O., Agboola, A.A.A., and Smarandache, F., "Refined Neutrosophic Rings II", International Journal of Neutrosophic Science, Vol. 2, pp. 89-94, 2020.
[10] Kandasamy V, Smarandache F., and Kandasamy I., Special Fuzzy Matrices for Social Scientists . Printed in the United States of America,2007, book, 99 pages.
[11] Abobala, M., Bal, M., Aswad, M., "A Short Note On Some Novel Applications of Semi Module Homomorphisms", International journal of neutrosophic science, 2022.
[12] Thomas, M. G., " Convergence of Powers of a Fuzzy Matrix", J. Math. Annal. Appl. 57 , pp. 476-480, 1977.
[13] Hatip, A., and Olgun, N., " On Refined Neutrosophic R-Module", International Journal of Neutrosophic Science, Vol. 7, pp.87-96, 2020.
[14] Ibrahim, M.A., Agboola, A.A.A, Badmus, B.S., and Akinleye, S.A. (2020). On refined Neutrosophic Vector Spaces II, International Journal of Neutrosophic Science, 9, 22-36.
[15] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings", Neutrosophic Sets and Systems, Vol. 45, 2021.
[16] Muhammad Saeed, Muhammad Saqlain, Asad Mehmood, Sonia Yaqoob, " Multi-Polar Neutrosophic Soft Sets With Application In Medical Diagnosis and Decision Making" Neutrosophic Sets and Systems, Vol. 33, pp. 183-207, 2020.
[17] Abobala, M., Partial Foundation of Neutrosophic Number Theory, Neutrosophic Sets and Systems, Vol. 39 , 2021.
[18] Khaled, H., and Younus, A., and Mohammad, A., " The Rectangle Neutrosophic Fuzzy Matrices", Faculty of Education Journal Vol. 15, 2019. (Arabic version)
[19] Sankari, H., and Abobala, M.," Neutrosophic Linear Diophantine Equations With two Variables", Neutrosophic Sets and Systems, Vol. 38, 2020.
[20] Agboola, A.A.A,. and Akinleye, S.A,. "Neutrosophic Vector Spaces", Neutrosophic Sets and Systems, Vol. 4 , pp. 9-17, 2014.
[21] Ibrahim, M.A., Agboola, A.A.A, Badmus, B.S., and Akinleye, S.A., "On refined Neutrosophic Vector Spaces I", International Journal of Neutrosophic Science, Vol. 7, pp. 97-109, 2020.
[22] Abobala, M., "On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations", Mathematical Problems in Engineering, Hindawi, 2021.
[23] T.Chalapathi and L. Madhavi,. "Neutrosophic Boolean Rings", Neutrosophic Sets and Systems, Vol. 33, pp. 57-66, 2020.
[24] Abobala, M., "Neutrosophic Real Inner Product Spaces", Neutrosophic Sets and Systems, Vol. 43, 2021.
[25] Abobala, M., " A Study Of Nil Ideals and Kothe's Conjecture In Neutrosophic Rings", International Journal of Mathematics and Mathematical Sciences", Hindawi, 2021
[26] Ramesh, K., " Ngbr Homomorphisms In Neutrosophic Topological Spaces", Neutrosophic Sets and Systems, Vol. 32, pp. 25-37, 2020.
[27] Olgun, N., Hatip, A., Bal, M., and Abobala, M., " A Novel Approach To Necessary and Sufficient Conditions For The Diagonalization of Refined Neutrosophic Matrices", International Journal of Neutrosophic Science, Vol. 16, pp. 72-79, 2021.
[28] Abobala, M., and Hatip, A., "An Algebraic Approch To Neutrosophic Euclidean Geometry", Neutrosophic Sets and Systems, Vol. 43, 2021.
[29] Ibrahim, M., and Abobala, M., "An Introduction To Refined Neutrosophic Number Theory", Neutrosophic Sets and Systems, Vol. 45, 2021.
[30] Aswad. F, M., " A Study of neutrosophic Bi Matrix", Neutrosophic Knowledge, Vol. 2, 2021.
[31] Ali, R., "A Short Note On The Solution of n-Refined Neutrosophic Linear Diophantine Equations", International Journal Of Neutrosophic Science, Vol. 15, 2021.
[32] Hajjari, A., and Ali, R., " A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings", International Journal of Neutrosophic Science", Vol. 16, 2021.
[33] Mukherjee, A., & Das, R. (2020). Neutrosophic Bipolar Vague Soft Set and Its Application to Decision Making Problems. Neutrosophic Sets and Systems, 32, 410-424.
[34] Das, R., & Tripathy, B.C. (2020). Neutrosophic Multiset Topological Space. Neutrosophic Sets and Systems, 35, 142-152.
[35] Smarandache, F. (2005) Neutrosophic set – A generalization of the intuitionistic fuzzy sets, International Journal of pure and Applied Mathematics, 24(3) , 287-297
