Comparison of defuzzification methods for fuzzy stochastic linear programming

The present study focused on comparison of three defuzzification methods in transforming fuzzy two-stage stochastic linear programming problem into a crisp problem. The fuzzy transformation techniques that utilized in this study were Yager’s robust ranking method, generalized mean integration repres...

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Main Author:	Gan, Siew Ling
Format:	Thesis
Language:	English
Published:	2014
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/53761/25/GanSiewLingMFS2014.pdf
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spelling	my-utm-ep.537612020-09-02T03:09:50Z Comparison of defuzzification methods for fuzzy stochastic linear programming 2014-06 Gan, Siew Ling QA Mathematics The present study focused on comparison of three defuzzification methods in transforming fuzzy two-stage stochastic linear programming problem into a crisp problem. The fuzzy transformation techniques that utilized in this study were Yager’s robust ranking method, generalized mean integration representation (GMIR) method, and centroid defuzzification method (CDM). Besides that, an assumption that the probability distribution obtained via expert was fuzzy and consisted only partial information was made. Five problems which modified based on Dakota’s Furniture Company were presented to give an illustration on how the fuzzy transformations using the three mentioned techniques were carried out. The defuzzified two-stage stochastic linear programming problems from each of the techniques were solved using a modelling system of GAMS, which implemented using a solver called DECIS. The difference between first problem and the rest of the problems was demand levels in first problem were symmetric triangular fuzzy numbers. Transformation of first problem using three different techniques resulted in getting the same model formulation, and hence the result obtained from GAMS/DECIS obviously was similar. The results of Problem 2 and Problem 3 obtained from the GAMS/DECIS showed a slight difference in resource quantities, production quantities, and the total profit, and CDM method showed the best optimum solutions. Meanwhile, GMIR method showed better optimum solutions in Problem 4 and 5. Hence, it can be concluded that CDM and GMIR are best methods of defuzzification for non-symmetric triangular fuzzy numbers problems comparing to Yager’s robust ranking method. 2014-06 Thesis http://eprints.utm.my/id/eprint/53761/ http://eprints.utm.my/id/eprint/53761/25/GanSiewLingMFS2014.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:85375 masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Gan, Siew Ling Comparison of defuzzification methods for fuzzy stochastic linear programming
description	The present study focused on comparison of three defuzzification methods in transforming fuzzy two-stage stochastic linear programming problem into a crisp problem. The fuzzy transformation techniques that utilized in this study were Yager’s robust ranking method, generalized mean integration representation (GMIR) method, and centroid defuzzification method (CDM). Besides that, an assumption that the probability distribution obtained via expert was fuzzy and consisted only partial information was made. Five problems which modified based on Dakota’s Furniture Company were presented to give an illustration on how the fuzzy transformations using the three mentioned techniques were carried out. The defuzzified two-stage stochastic linear programming problems from each of the techniques were solved using a modelling system of GAMS, which implemented using a solver called DECIS. The difference between first problem and the rest of the problems was demand levels in first problem were symmetric triangular fuzzy numbers. Transformation of first problem using three different techniques resulted in getting the same model formulation, and hence the result obtained from GAMS/DECIS obviously was similar. The results of Problem 2 and Problem 3 obtained from the GAMS/DECIS showed a slight difference in resource quantities, production quantities, and the total profit, and CDM method showed the best optimum solutions. Meanwhile, GMIR method showed better optimum solutions in Problem 4 and 5. Hence, it can be concluded that CDM and GMIR are best methods of defuzzification for non-symmetric triangular fuzzy numbers problems comparing to Yager’s robust ranking method.
format	Thesis
qualification_level	Master's degree
author	Gan, Siew Ling
author_facet	Gan, Siew Ling
author_sort	Gan, Siew Ling
title	Comparison of defuzzification methods for fuzzy stochastic linear programming
title_short	Comparison of defuzzification methods for fuzzy stochastic linear programming
title_full	Comparison of defuzzification methods for fuzzy stochastic linear programming
title_fullStr	Comparison of defuzzification methods for fuzzy stochastic linear programming
title_full_unstemmed	Comparison of defuzzification methods for fuzzy stochastic linear programming
title_sort	comparison of defuzzification methods for fuzzy stochastic linear programming
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2014
url	http://eprints.utm.my/id/eprint/53761/25/GanSiewLingMFS2014.pdf
_version_	1747817622140878848

Comparison of defuzzification methods for fuzzy stochastic linear programming

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