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...

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Main Author: Wan Suhana, Wan Daud
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
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spelling my-uum-etd.102072023-01-11T00:44:43Z 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 left-right triangular fuzzy numbers (LR-TFN), which either positive, negative or near-zero. 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 near-zero LR-TFN as the coefficients of the equations. The constructed methods also utilized the Kronecker product and Vec-operator 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 non-singular 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 2024-03-02 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 left-right triangular fuzzy numbers (LR-TFN), which either positive, negative or near-zero. 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 near-zero LR-TFN as the coefficients of the equations. The constructed methods also utilized the Kronecker product and Vec-operator 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 non-singular 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
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