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

S. Obaid Jameel¹, A. Mahdi Salih², R. Adnan Jaleel³, Musaddak M. A. Zahra⁴

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

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

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

⁴Al-Mustaqbal University College, Department  of Computer Technology Engineering, Babylon,  Iraq

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

Emails: sjameel@uowasit.edu.iq; amahdi@uowasit.edu.iq; iraq_it_2010@yahoo.com; musaddaqmahir@mustaqbal-college.edu.iq

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.