Solving sylvester matrix equations with LR bipolar triangular fuzzy numbers in electric circuits problems

Bipolar crisp numbers refer to two different functions and information in a given system, namely positive and negative components. Likelihood and unlikelihood information can be simultaneously represented by bipolar crisp numbers rather than classical crisp numbers. However, since bipolar crisp numb...

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Main Author:	Cheah Soo Thape, Neendha
Format:	Thesis
Language:	eng eng
Published:	2022
Subjects:	QA76.76 Fuzzy System.
Online Access:	https://etd.uum.edu.my/10167/1/s826422_01.pdf https://etd.uum.edu.my/10167/2/s826422_02.pdf
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spelling	my-uum-etd.101672022-12-19T09:54:32Z Solving sylvester matrix equations with LR bipolar triangular fuzzy numbers in electric circuits problems 2022 Cheah Soo Thape, Neendha Ahmad, Nazihah Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences QA76.76 Fuzzy System. Bipolar crisp numbers refer to two different functions and information in a given system, namely positive and negative components. Likelihood and unlikelihood information can be simultaneously represented by bipolar crisp numbers rather than classical crisp numbers. However, since bipolar crisp numbers are inadequate in dealing with uncertainty problem, bipolar fuzzy numbers (BFN) are used instead. BFN in Sylvester matrix equations (SME) plays an essential role in the control system such as in electrical controller. An electrical controller of RLC circuit consisting of resistor (R), inductor (L), and capacitor (C), is used to control the amount of electric currents flowing across the electric circuits. Besides, complex numbers which consist of real and imaginary parts are used in solving RLC circuit, where real numbers denote resistance, while imaginary numbers denote inductance or capacitance. To the best of our knowledge, the integration of SME with either BFN or complex BFN is not yet explored. Therefore, this study aims to construct analytical approaches in solving bipolar fuzzy Sylvester matrix equation (FSME), complex bipolar FSME, bipolar fully fuzzy Sylvester matrix equation (FFSME), and complex bipolar fully fuzzy linear system (FFLS) in left-right (LR) bipolar triangular fuzzy numbers. In order to obtain the solutions, bipolar FSME, complex bipolar FSME, and bipolar FFSME are converted into the bipolar linear system by utilizing Kronecker product and Vecoperator. Next, an equivalent bipolar linear system (EBLS), equivalent complex bipolar linear system (ECBLS), associated bipolar linear system (ABLS), and associated complex bipolar linear system (ACBLS) are established. Then, the final solutions of the constructed methods are obtained using inverse method. Therefore, four analytical approaches have been constructed in solving bipolar FSME, complex bipolar FSME, bipolar FFSME, and complex bipolar FFLS in LR forms. Several examples are presented to illustrate the constructed methods. Moreover, the application of RLC circuits with complex bipolar FSME and complex bipolar FFLS are also carried out. In conclusion, the new findings of analytical approaches add to the fuzzy equations body of knowledge with significant applications in bipolar electrical controllers. 2022 Thesis https://etd.uum.edu.my/10167/ https://etd.uum.edu.my/10167/1/s826422_01.pdf text eng 2025-03-06 staffonly https://etd.uum.edu.my/10167/2/s826422_02.pdf text eng public other masters Universiti Utara Malaysia
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng
advisor	Ahmad, Nazihah
topic	QA76.76 Fuzzy System.
spellingShingle	QA76.76 Fuzzy System. Cheah Soo Thape, Neendha Solving sylvester matrix equations with LR bipolar triangular fuzzy numbers in electric circuits problems
description	Bipolar crisp numbers refer to two different functions and information in a given system, namely positive and negative components. Likelihood and unlikelihood information can be simultaneously represented by bipolar crisp numbers rather than classical crisp numbers. However, since bipolar crisp numbers are inadequate in dealing with uncertainty problem, bipolar fuzzy numbers (BFN) are used instead. BFN in Sylvester matrix equations (SME) plays an essential role in the control system such as in electrical controller. An electrical controller of RLC circuit consisting of resistor (R), inductor (L), and capacitor (C), is used to control the amount of electric currents flowing across the electric circuits. Besides, complex numbers which consist of real and imaginary parts are used in solving RLC circuit, where real numbers denote resistance, while imaginary numbers denote inductance or capacitance. To the best of our knowledge, the integration of SME with either BFN or complex BFN is not yet explored. Therefore, this study aims to construct analytical approaches in solving bipolar fuzzy Sylvester matrix equation (FSME), complex bipolar FSME, bipolar fully fuzzy Sylvester matrix equation (FFSME), and complex bipolar fully fuzzy linear system (FFLS) in left-right (LR) bipolar triangular fuzzy numbers. In order to obtain the solutions, bipolar FSME, complex bipolar FSME, and bipolar FFSME are converted into the bipolar linear system by utilizing Kronecker product and Vecoperator. Next, an equivalent bipolar linear system (EBLS), equivalent complex bipolar linear system (ECBLS), associated bipolar linear system (ABLS), and associated complex bipolar linear system (ACBLS) are established. Then, the final solutions of the constructed methods are obtained using inverse method. Therefore, four analytical approaches have been constructed in solving bipolar FSME, complex bipolar FSME, bipolar FFSME, and complex bipolar FFLS in LR forms. Several examples are presented to illustrate the constructed methods. Moreover, the application of RLC circuits with complex bipolar FSME and complex bipolar FFLS are also carried out. In conclusion, the new findings of analytical approaches add to the fuzzy equations body of knowledge with significant applications in bipolar electrical controllers.
format	Thesis
qualification_name	other
qualification_level	Master's degree
author	Cheah Soo Thape, Neendha
author_facet	Cheah Soo Thape, Neendha
author_sort	Cheah Soo Thape, Neendha
title	Solving sylvester matrix equations with LR bipolar triangular fuzzy numbers in electric circuits problems
title_short	Solving sylvester matrix equations with LR bipolar triangular fuzzy numbers in electric circuits problems
title_full	Solving sylvester matrix equations with LR bipolar triangular fuzzy numbers in electric circuits problems
title_fullStr	Solving sylvester matrix equations with LR bipolar triangular fuzzy numbers in electric circuits problems
title_full_unstemmed	Solving sylvester matrix equations with LR bipolar triangular fuzzy numbers in electric circuits problems
title_sort	solving sylvester matrix equations with lr bipolar triangular fuzzy numbers in electric circuits problems
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2022
url	https://etd.uum.edu.my/10167/1/s826422_01.pdf https://etd.uum.edu.my/10167/2/s826422_02.pdf
_version_	1776103756656541696

Solving sylvester matrix equations with LR bipolar triangular fuzzy numbers in electric circuits problems

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