# 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: Thesis engeng 2021 https://etd.uum.edu.my/10207/1/s901088_01.pdf https://etd.uum.edu.my/10207/2/s901088_02.pdf No Tags, Be the first to tag this record!
id my-uum-etd.10207 uketd_dc 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 Universiti Utara Malaysia UUM ETD eng eng Ahmad, Nazihah Malkawi, Ghassan Omar Mahmoud QA76.76 Fuzzy System. QA76.76 Fuzzy System. Wan Suhana, Wan Daud 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 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. Thesis other Doctorate Wan Suhana, Wan Daud Wan Suhana, Wan Daud Wan Suhana, Wan Daud Solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations Solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations Solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations Solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations Solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations Universiti Utara Malaysia Awang Had Salleh Graduate School of Arts & Sciences 2021 https://etd.uum.edu.my/10207/1/s901088_01.pdf https://etd.uum.edu.my/10207/2/s901088_02.pdf 1776103765946925056