Solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations
Control system theory often involved the application of matrix equations and pair matrix equations where there are possibilities that uncertainty conditions can exist. In this case, the classical matrix equations and pair matrix equations are not well equipped to handle these conditions. Even though...
Saved in:
Main Author:  

Format:  Thesis 
Language:  eng eng 
Published: 
2021

Subjects:  
Online Access:  https://etd.uum.edu.my/10207/1/s901088_01.pdf https://etd.uum.edu.my/10207/2/s901088_02.pdf 
Tags: 
Add Tag
No Tags, Be the first to tag this record!

id 
myuumetd.10207 

record_format 
uketd_dc 
spelling 
myuumetd.1020720230111T00:44:43Z Solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations 2021 Wan Suhana, Wan Daud Ahmad, Nazihah Malkawi, Ghassan Omar Mahmoud Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts & Sciences QA76.76 Fuzzy System. Control system theory often involved the application of matrix equations and pair matrix equations where there are possibilities that uncertainty conditions can exist. In this case, the classical matrix equations and pair matrix equations are not well equipped to handle these conditions. Even though there are some previous studies in solving the matrix equations and pair matrix equations with uncertainty conditions, there are some limitations that include the fuzzy arithmetic operations, the type of fuzzy coefficients and the singularity of matrix coefficients. Therefore, this study aims to construct new methods for solving matrix equations and pair matrix equations with all the coefficients of the matrix equations are arbitrary leftright triangular fuzzy numbers (LRTFN), which either positive, negative or nearzero. In constructing these methods, some modifications on the existing fuzzy subtraction and multiplication arithmetic operators are necessary. By modifying the existing fuzzy arithmetic operators, the constructed methods exceed the positive restriction to allow the negative and nearzero LRTFN as the coefficients of the equations. The constructed methods also utilized the Kronecker product and Vecoperator in transforming the fully fuzzy matrix equations and pair fully fuzzy matrix equations to a simpler form of equations. On top of that, new associated linear systems are developed based on the modified fuzzy multiplication arithmetic operators. The constructed methods are verified by presenting some numerical examples. As a result, the constructed methods have successfully demonstrated the solutions for the arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations, with minimum complexity of the fuzzy operations. The constructed methods are applicable for singular and nonsingular matrices regardless of the size of the matrix. With that, the constructed methods are considered as a new contribution to the application of control system theory. 2021 Thesis https://etd.uum.edu.my/10207/ https://etd.uum.edu.my/10207/1/s901088_01.pdf text eng 20240302 staffonly https://etd.uum.edu.my/10207/2/s901088_02.pdf text eng public other doctoral Universiti Utara Malaysia 
institution 
Universiti Utara Malaysia 
collection 
UUM ETD 
language 
eng eng 
advisor 
Ahmad, Nazihah Malkawi, Ghassan Omar Mahmoud 
topic 
QA76.76 Fuzzy System. 
spellingShingle 
QA76.76 Fuzzy System. Wan Suhana, Wan Daud Solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations 
description 
Control system theory often involved the application of matrix equations and pair matrix equations where there are possibilities that uncertainty conditions can exist. In this case, the classical matrix equations and pair matrix equations are not well equipped to handle these conditions. Even though there are some previous studies in solving the matrix equations and pair matrix equations with uncertainty conditions, there are some limitations that include the fuzzy arithmetic operations, the type of fuzzy coefficients and the singularity of matrix coefficients. Therefore, this study aims to construct new methods for solving matrix equations and pair matrix equations with all the coefficients of the matrix equations are arbitrary leftright triangular fuzzy numbers (LRTFN), which either positive, negative or nearzero. In constructing these methods, some modifications on the existing fuzzy subtraction and multiplication arithmetic operators are necessary. By modifying the existing fuzzy arithmetic operators, the constructed methods exceed the positive restriction to allow the negative and nearzero LRTFN as the coefficients of the equations. The constructed methods also utilized the Kronecker product and Vecoperator in transforming the fully fuzzy matrix equations and pair fully fuzzy matrix equations to a simpler form of equations. On top of that, new associated linear systems are developed based on the modified fuzzy multiplication arithmetic operators. The constructed methods are verified by presenting some numerical examples. As a result, the constructed methods have successfully demonstrated the solutions for the arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations, with minimum complexity of the fuzzy operations. The constructed methods are applicable for singular and nonsingular matrices regardless of the size of the matrix. With that, the constructed methods are considered as a new contribution to the application of control system theory. 
format 
Thesis 
qualification_name 
other 
qualification_level 
Doctorate 
author 
Wan Suhana, Wan Daud 
author_facet 
Wan Suhana, Wan Daud 
author_sort 
Wan Suhana, Wan Daud 
title 
Solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations 
title_short 
Solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations 
title_full 
Solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations 
title_fullStr 
Solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations 
title_full_unstemmed 
Solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations 
title_sort 
solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations 
granting_institution 
Universiti Utara Malaysia 
granting_department 
Awang Had Salleh Graduate School of Arts & Sciences 
publishDate 
2021 
url 
https://etd.uum.edu.my/10207/1/s901088_01.pdf https://etd.uum.edu.my/10207/2/s901088_02.pdf 
_version_ 
1776103765946925056 