Unrestricted solutions of arbitrary linear fuzzy systems

Solving linear fuzzy system has intrigued many researchers due to its ability to handle imprecise information of real problems. However, there are several weaknesses of the existing methods. Among the drawbacks are heavy dependence on linear programing, avoidance of near zero fuzzy numbers, lack of...

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Main Author:	O.Malkawi, Ghassan
Format:	Thesis
Language:	eng eng
Published:	2015
Subjects:	QA76.76 Fuzzy System.
Online Access:	https://etd.uum.edu.my/5779/1/depositpermission_s93740.pdf https://etd.uum.edu.my/5779/2/s93740_01.pdf
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id	my-uum-etd.5779
record_format	uketd_dc
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng
advisor	Ahmad, Nazihah Ibrahim, Haslinda
topic	QA76.76 Fuzzy System.
spellingShingle	QA76.76 Fuzzy System. O.Malkawi, Ghassan Unrestricted solutions of arbitrary linear fuzzy systems
description	Solving linear fuzzy system has intrigued many researchers due to its ability to handle imprecise information of real problems. However, there are several weaknesses of the existing methods. Among the drawbacks are heavy dependence on linear programing, avoidance of near zero fuzzy numbers, lack of accurate solutions, focus on limited size of the systems, and restriction to the matrix coefficients and solutions. Therefore, this study aims to construct new methods which are associated linear systems, min-max system and absolute systems in matrix theory with triangular fuzzy numbers to solve linear fuzzy systems with respect to the aforementioned drawbacks. It is proven that the new constructed associated linear systems are equivalent to linear fuzzy systems without involving any fuzzy operation. Furthermore, the new constructed associated linear systems are effective in providing exact solution as compared to linear programming, which is subjected to a number of constraints. These methods are also able to provide accurate solutions for large systems. Moreover, the existence of fuzzy solutions and classification of possible solutions are being checked by these associated linear systems. In case of near zero fully fuzzy linear system, fuzzy operations are required to determine the nature of solution of fuzzy system and to ensure the fuzziness of the solution. Finite solutions which are new concept of consistency in linear systems are obtained by the constructed min-max and absolute systems. These developed methods can also be modified to solve advanced fuzzy systems such as fully fuzzy matrix equation and fully fuzzy Sylvester equation, and can be employed for other types of fuzzy numbers such as trapezoidal fuzzy number. The study contributes to the methods to solve arbitrary linear fuzzy systems without any restriction on the system.
format	Thesis
qualification_name	Ph.D.
qualification_level	Doctorate
author	O.Malkawi, Ghassan
author_facet	O.Malkawi, Ghassan
author_sort	O.Malkawi, Ghassan
title	Unrestricted solutions of arbitrary linear fuzzy systems
title_short	Unrestricted solutions of arbitrary linear fuzzy systems
title_full	Unrestricted solutions of arbitrary linear fuzzy systems
title_fullStr	Unrestricted solutions of arbitrary linear fuzzy systems
title_full_unstemmed	Unrestricted solutions of arbitrary linear fuzzy systems
title_sort	unrestricted solutions of arbitrary linear fuzzy systems
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2015
url	https://etd.uum.edu.my/5779/1/depositpermission_s93740.pdf https://etd.uum.edu.my/5779/2/s93740_01.pdf
_version_	1747827980088901632
spelling	my-uum-etd.57792022-04-09T23:03:37Z Unrestricted solutions of arbitrary linear fuzzy systems 2015 O.Malkawi, Ghassan Ahmad, Nazihah Ibrahim, Haslinda Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences QA76.76 Fuzzy System. Solving linear fuzzy system has intrigued many researchers due to its ability to handle imprecise information of real problems. However, there are several weaknesses of the existing methods. Among the drawbacks are heavy dependence on linear programing, avoidance of near zero fuzzy numbers, lack of accurate solutions, focus on limited size of the systems, and restriction to the matrix coefficients and solutions. Therefore, this study aims to construct new methods which are associated linear systems, min-max system and absolute systems in matrix theory with triangular fuzzy numbers to solve linear fuzzy systems with respect to the aforementioned drawbacks. It is proven that the new constructed associated linear systems are equivalent to linear fuzzy systems without involving any fuzzy operation. Furthermore, the new constructed associated linear systems are effective in providing exact solution as compared to linear programming, which is subjected to a number of constraints. These methods are also able to provide accurate solutions for large systems. Moreover, the existence of fuzzy solutions and classification of possible solutions are being checked by these associated linear systems. In case of near zero fully fuzzy linear system, fuzzy operations are required to determine the nature of solution of fuzzy system and to ensure the fuzziness of the solution. Finite solutions which are new concept of consistency in linear systems are obtained by the constructed min-max and absolute systems. These developed methods can also be modified to solve advanced fuzzy systems such as fully fuzzy matrix equation and fully fuzzy Sylvester equation, and can be employed for other types of fuzzy numbers such as trapezoidal fuzzy number. The study contributes to the methods to solve arbitrary linear fuzzy systems without any restriction on the system. 2015 Thesis https://etd.uum.edu.my/5779/ https://etd.uum.edu.my/5779/1/depositpermission_s93740.pdf text eng public https://etd.uum.edu.my/5779/2/s93740_01.pdf text eng public Ph.D. doctoral Universiti Utara Malaysia Abadir, K. M., & Magnus, J. R. (2005). Matrix algebra (Vol. 1). Cambridge University Press. Abbasbandy, S., & Hashemi, M. S. (2012). Solving fully fuzzy linear systems by using implicit Gauss–Cholesky algorithm. Computational mathematics and modeling, 23(1), 107-124. Abdolmaleki, E., & Edalatpanah, S. A. (2014). Chebyshev Semi-iterative Method to Solve Fully Fuzzy linear Systems. 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Unrestricted solutions of arbitrary linear fuzzy systems

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