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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.537612020-09-02T03:09:50Z http://eprints.utm.my/id/eprint/53761/ Comparison of defuzzification methods for fuzzy stochastic linear programming 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 NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/53761/25/GanSiewLingMFS2014.pdf Gan, Siew Ling (2014) Comparison of defuzzification methods for fuzzy stochastic linear programming. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science. http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:85375
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
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
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
publishDate 2014
url http://eprints.utm.my/id/eprint/53761/25/GanSiewLingMFS2014.pdf
http://eprints.utm.my/id/eprint/53761/
http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:85375
_version_ 1677781093293490176
score 13.211869

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