Defuzzification of groups of fuzzy numbers using data envelopment analysis

Defuzzification is a critical process in the implementation of fuzzy systems that converts fuzzy numbers to crisp representations. Few researchers have focused on cases where the crisp outputs must satisfy a set of relationships dictated in the original crisp data. This phenomenon indicates that th...

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Main Author:	Al-Ogaidi, Jehan Saleh Ahmed
Format:	Thesis
Language:	eng eng
Published:	2016
Subjects:	QA299.6-433 Analysis QA76.76 Fuzzy System.
Online Access:	https://etd.uum.edu.my/6015/1/s93607_01.pdf https://etd.uum.edu.my/6015/2/s93607_02.pdf
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id	my-uum-etd.6015
record_format	uketd_dc
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng
advisor	Mat Kasim, Maznah Madjid, Zerafat Angiz E. Langroudi
topic	QA299.6-433 Analysis QA76.76 Fuzzy System.
spellingShingle	QA299.6-433 Analysis QA76.76 Fuzzy System. Al-Ogaidi, Jehan Saleh Ahmed Defuzzification of groups of fuzzy numbers using data envelopment analysis
description	Defuzzification is a critical process in the implementation of fuzzy systems that converts fuzzy numbers to crisp representations. Few researchers have focused on cases where the crisp outputs must satisfy a set of relationships dictated in the original crisp data. This phenomenon indicates that these crisp outputs are mathematically dependent on one another. Furthermore, these fuzzy numbers may exist as a group of fuzzy numbers. Therefore, the primary aim of this thesis is to develop a method to defuzzify groups of fuzzy numbers based on Charnes, Cooper, and Rhodes (CCR)-Data Envelopment Analysis (DEA) model by modifying the Center of Gravity (COG) method as the objective function. The constraints represent the relationships and some additional restrictions on the allowable crisp outputs with their dependency property. This leads to the creation of crisp values with preserved relationships and/or properties as in the original crisp data. Comparing with Linear Programming (LP) based model, the proposed CCR-DEA model is more efficient, and also able to defuzzify non-linear fuzzy numbers with accurate solutions. Moreover, the crisp outputs obtained by the proposed method are the nearest points to the fuzzy numbers in case of crisp independent outputs, and best nearest points to the fuzzy numbers in case of dependent crisp outputs. As a conclusion, the proposed CCR-DEA defuzzification method can create either dependent crisp outputs with preserved relationship or independent crisp outputs without any relationship. Besides, the proposed method is a general method to defuzzify groups or individuals fuzzy numbers under the assumption of convexity with linear and non-linear membership functions or relationships.
format	Thesis
qualification_name	Ph.D.
qualification_level	Doctorate
author	Al-Ogaidi, Jehan Saleh Ahmed
author_facet	Al-Ogaidi, Jehan Saleh Ahmed
author_sort	Al-Ogaidi, Jehan Saleh Ahmed
title	Defuzzification of groups of fuzzy numbers using data envelopment analysis
title_short	Defuzzification of groups of fuzzy numbers using data envelopment analysis
title_full	Defuzzification of groups of fuzzy numbers using data envelopment analysis
title_fullStr	Defuzzification of groups of fuzzy numbers using data envelopment analysis
title_full_unstemmed	Defuzzification of groups of fuzzy numbers using data envelopment analysis
title_sort	defuzzification of groups of fuzzy numbers using data envelopment analysis
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2016
url	https://etd.uum.edu.my/6015/1/s93607_01.pdf https://etd.uum.edu.my/6015/2/s93607_02.pdf
_version_	1747828007276380160
spelling	my-uum-etd.60152021-04-05T01:48:25Z Defuzzification of groups of fuzzy numbers using data envelopment analysis 2016 Al-Ogaidi, Jehan Saleh Ahmed Mat Kasim, Maznah Madjid, Zerafat Angiz E. Langroudi Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences QA299.6-433 Analysis QA76.76 Fuzzy System. Defuzzification is a critical process in the implementation of fuzzy systems that converts fuzzy numbers to crisp representations. Few researchers have focused on cases where the crisp outputs must satisfy a set of relationships dictated in the original crisp data. This phenomenon indicates that these crisp outputs are mathematically dependent on one another. Furthermore, these fuzzy numbers may exist as a group of fuzzy numbers. Therefore, the primary aim of this thesis is to develop a method to defuzzify groups of fuzzy numbers based on Charnes, Cooper, and Rhodes (CCR)-Data Envelopment Analysis (DEA) model by modifying the Center of Gravity (COG) method as the objective function. The constraints represent the relationships and some additional restrictions on the allowable crisp outputs with their dependency property. This leads to the creation of crisp values with preserved relationships and/or properties as in the original crisp data. Comparing with Linear Programming (LP) based model, the proposed CCR-DEA model is more efficient, and also able to defuzzify non-linear fuzzy numbers with accurate solutions. Moreover, the crisp outputs obtained by the proposed method are the nearest points to the fuzzy numbers in case of crisp independent outputs, and best nearest points to the fuzzy numbers in case of dependent crisp outputs. As a conclusion, the proposed CCR-DEA defuzzification method can create either dependent crisp outputs with preserved relationship or independent crisp outputs without any relationship. Besides, the proposed method is a general method to defuzzify groups or individuals fuzzy numbers under the assumption of convexity with linear and non-linear membership functions or relationships. 2016 Thesis https://etd.uum.edu.my/6015/ https://etd.uum.edu.my/6015/1/s93607_01.pdf text eng public https://etd.uum.edu.my/6015/2/s93607_02.pdf text eng public Ph.D. doctoral Universiti Utara Malaysia Abbasbandy, S., & Asady, B. (2006). Ranking of fuzzy numbers by sign distance. Information Sciences, 176(16), 2405–2416. doi:10.1016/j.ins.2005.03.013 Abbasbandy, S., & Hajjari, T. (2009). A new approach for ranking of trapezoidal fuzzy numbers. Computers & Mathematics with Applications, 57(3), 413–419. doi:10.1016/j.camwa.2008.10.090 Abdullah, N. H. (2014). Making space at hospitals (KKM) health DG Malaysia. 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