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International Journal of Neutrosophic Science
Volume 19 , Issue 1, PP: 267-271 , 2022 | Cite this article as | XML | Html |PDF

Title

On The Neutrosophic Formula of Some Matrix Equations Derived from Data Mining Theory and Control Systems

Authors Names :   S. Obaid Jameel   1 *     A. Mahdi Salih   2     R. Adnan Jaleel   3     Musaddak M. A. Zahra   4  

1  Affiliation :  University of Wasit, College of Education for Pure Sciences, Mathematics department, Wasit, Iraq

    Email :  sjameel@uowasit.edu.iq


2  Affiliation :  Wasit University, College of Administration and Economics, Statistics Department, Wasit, Iraq

    Email :  amahdi@uowasit.edu.iq


3  Affiliation :  Al-Nahrain University, Department of Information and Communication Engineering, Baghdad, Iraq

    Email :  iraq_it_2010@yahoo.com


4  Affiliation :  Unvirsity of Babylon, Department of Electrical Engineering, Babylon, Iraq

    Email :  musaddaqmahir@mustaqbal-college.edu.iq



Doi   :   https://doi.org/10.54216/IJNS.190122

Received: March 04, 2022 Accepted: September 16, 2022

Abstract :

This paper is dedicated to studying the neutrosophic formula of some famous matrix equations used in theoretical data mining algorithms and control systems by using neutrosophic matrices and refined neutrosophic matrices over neutrosophic real fields. On the other hand, we concentrate on the neutrosophic formula of the Sylvester equation, and Lyapunov equation, where we study their formulas and properties in terms of theorems in the neutrosophic real number field and refined real number field. Also, we illustrate many different examples to clarify the validity of our work.

Keywords :

Data mining; Control System; Matrix equation; Neutrosophic matrix; Refined neutrosophic matrix.

References :

[1] R. Bartels and G. W. Stewart. Solution of the matrix equation AX + XB = C. Comm A.C.M.,

15(9):820–826, 1972.

[2] L. Grubiši´c and D. Kressner. On the eigenvalue decay of solutions to operator Lyapunov equations.

Syst. Control Lett., 73:42–47, 2014.

[3] Abobala, M., Bal, M., and Hatip, A., "A Review On Recent Advantages In Algebraic Theory Of

Neutrosophic Matrices", International Journal of Neutrosophic Science, Vol. 17, 2021.

[4] 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.

[5] 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.

[6] Abobala, M., On The Representation of Neutrosophic Matrices by Neutrosophic Linear

Transformations, Journal of Mathematics, Hindawi, 2021.

[7] Prem Kumar Singh, A Note on Basic Proof of Some Famous Mathematical Theorem and Its

Illustration, Journal of Neutrosophic and Fuzzy Systems, Vol. 3 , No. 1 , (2022) : 39-53

[8] Abobala, M., "On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined

Neutrosophic Linear Equations", Mathematical Problems in Engineering, Hindawi, 2021

[9] E.O. Adeleke , A.A.A. Agboola , F. Smarandache, Refined Neutrosophic Rings II, International Journal

of Neutrosophic Science, Vol. 2 , No. 2 , (2020) : 89-94.

[10] Mikail Bal , Katy D. Ahmad , Rozina Ali, A Review On Recent Developments In Neutrosophic Linear

Diophantine Equations, Journal of Neutrosophic and Fuzzy Systems, Vol. 2 , No. 1 , (2022) : 61-75

[11] V. Simoncini. A new iterative method for solving large-scale Lyapunov matrix equations. SIAM J. Sci.

Comput., 29(3):1268–1288, 2007.

[12] T. Stykel. Stability and inertia theorems for generalized Lyapunov equations. Linear Algebra Appl.,

355:297–314, 2002.

[13] Smarandache, F., " n-Valued Refined Neutrosophic Logic and Its Applications in Physics", Progress in

Physics, 143-146, Vol. 4, 2013.


Cite this Article as :
S. Obaid Jameel , A. Mahdi Salih , R. Adnan Jaleel , Musaddak M. A. Zahra, On The Neutrosophic Formula of Some Matrix Equations Derived from Data Mining Theory and Control Systems, International Journal of Neutrosophic Science, Vol. 19 , No. 1 , (2022) : 267-271 (Doi   :  https://doi.org/10.54216/IJNS.190122)