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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2016
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| Online Access: | https://etd.uum.edu.my/6015/1/s93607_01.pdf https://etd.uum.edu.my/6015/2/s93607_02.pdf https://etd.uum.edu.my/6015/ |
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| author | Al-Ogaidi, Jehan Saleh Ahmed |
| author_facet | Al-Ogaidi, Jehan Saleh Ahmed |
| author_sort | Al-Ogaidi, Jehan Saleh Ahmed |
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| content_provider | Universiti Utara Malaysia |
| content_source | UUM Electronic Theses |
| continent | Asia |
| country | Malaysia |
| 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 |
| id | my.uum.etd-6015 |
| institution | Universiti Utara Malaysia |
| language | en en |
| publishDate | 2016 |
| record_format | eprints |
| spelling | my.uum.etd-60152021-04-05T01:48:25Z https://etd.uum.edu.my/6015/ Defuzzification of groups of fuzzy numbers using data envelopment analysis Al-Ogaidi, Jehan Saleh Ahmed 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 NonPeerReviewed text en https://etd.uum.edu.my/6015/1/s93607_01.pdf text en https://etd.uum.edu.my/6015/2/s93607_02.pdf Al-Ogaidi, Jehan Saleh Ahmed (2016) Defuzzification of groups of fuzzy numbers using data envelopment analysis. PhD. thesis, Universiti Utara Malaysia. |
| spellingShingle | QA299.6-433 Analysis QA76.76 Fuzzy System. Al-Ogaidi, Jehan Saleh Ahmed Defuzzification of groups of fuzzy numbers using data envelopment analysis |
| title | 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_short | Defuzzification of groups of fuzzy numbers using data envelopment analysis |
| title_sort | defuzzification of groups of fuzzy numbers using data envelopment analysis |
| topic | QA299.6-433 Analysis QA76.76 Fuzzy System. |
| url | https://etd.uum.edu.my/6015/1/s93607_01.pdf https://etd.uum.edu.my/6015/2/s93607_02.pdf https://etd.uum.edu.my/6015/ |
| url_provider | http://etd.uum.edu.my/ |