A Note on Two-Stage Fuzzy Location Problems Under VaR Criterion With Irregular Fuzzy Variables
Recently, Yang <italic>et al.</italic> (Computers & Industrial Engineering, 131: 157–171, 2019) proposed a solution approach to the two-stage fuzzy location problem under the Value-at-Risk (VaR) criterion, which significantly reduced the computational complexity com...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9115014/ |
| _version_ | 1797776913480024064 |
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| author | Ke Wang Yuanyuan Wang Yan Yang Mark Goh |
| author_facet | Ke Wang Yuanyuan Wang Yan Yang Mark Goh |
| author_sort | Ke Wang |
| collection | DOAJ |
| description | Recently, Yang <italic>et al.</italic> (Computers & Industrial Engineering, 131: 157–171, 2019) proposed a solution approach to the two-stage fuzzy location problem under the Value-at-Risk (VaR) criterion, which significantly reduced the computational complexity compared with the other approximation treatments. However, in their work, the approach was developed for cases with regular fuzzy variables, which renders it useless when dealing with other types of fuzzy parameters such as discrete fuzzy variables and trapezoidal fuzzy numbers. In this note, for the general case involving arbitrary types of fuzzy parameters, we show that the VaR of a location decision can be determined exactly by solving a corresponding deterministic linear programming. Consequently, a similar approach is developed for the generalized case. Utilizing the extended approach, we show that the discrete case presented by Yang <italic>et al.</italic> can be solved directly rather than by enumerating all possible scenarios. Furthermore, a numerical example with regular fuzzy variables studied in their work is extended to the continuous but irregular case to illustrate our extension. |
| first_indexed | 2024-03-12T22:56:37Z |
| format | Article |
| id | doaj.art-243c3525753a4c699beb56b43f616157 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-12T22:56:37Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-243c3525753a4c699beb56b43f6161572023-07-19T23:00:56ZengIEEEIEEE Access2169-35362020-01-01811030611031510.1109/ACCESS.2020.30015899115014A Note on Two-Stage Fuzzy Location Problems Under VaR Criterion With Irregular Fuzzy VariablesKe Wang0Yuanyuan Wang1Yan Yang2https://orcid.org/0000-0001-7087-617XMark Goh3https://orcid.org/0000-0002-3620-7658School of Management, Shanghai University, Shanghai, ChinaSchool of Management, Shanghai University, Shanghai, ChinaFaculty of Economics and Business, KU Leuven, Leuven, BelgiumDepartment of Analytics and Operations, NUS Business School, National University of Singapore, SingaporeRecently, Yang <italic>et al.</italic> (Computers & Industrial Engineering, 131: 157–171, 2019) proposed a solution approach to the two-stage fuzzy location problem under the Value-at-Risk (VaR) criterion, which significantly reduced the computational complexity compared with the other approximation treatments. However, in their work, the approach was developed for cases with regular fuzzy variables, which renders it useless when dealing with other types of fuzzy parameters such as discrete fuzzy variables and trapezoidal fuzzy numbers. In this note, for the general case involving arbitrary types of fuzzy parameters, we show that the VaR of a location decision can be determined exactly by solving a corresponding deterministic linear programming. Consequently, a similar approach is developed for the generalized case. Utilizing the extended approach, we show that the discrete case presented by Yang <italic>et al.</italic> can be solved directly rather than by enumerating all possible scenarios. Furthermore, a numerical example with regular fuzzy variables studied in their work is extended to the continuous but irregular case to illustrate our extension.https://ieeexplore.ieee.org/document/9115014/Discrete fuzzy variablefacility location problemtrapezoidal fuzzy numbertwo-stage fuzzy programmingvalue-at-risk |
| spellingShingle | Ke Wang Yuanyuan Wang Yan Yang Mark Goh A Note on Two-Stage Fuzzy Location Problems Under VaR Criterion With Irregular Fuzzy Variables IEEE Access Discrete fuzzy variable facility location problem trapezoidal fuzzy number two-stage fuzzy programming value-at-risk |
| title | A Note on Two-Stage Fuzzy Location Problems Under VaR Criterion With Irregular Fuzzy Variables |
| title_full | A Note on Two-Stage Fuzzy Location Problems Under VaR Criterion With Irregular Fuzzy Variables |
| title_fullStr | A Note on Two-Stage Fuzzy Location Problems Under VaR Criterion With Irregular Fuzzy Variables |
| title_full_unstemmed | A Note on Two-Stage Fuzzy Location Problems Under VaR Criterion With Irregular Fuzzy Variables |
| title_short | A Note on Two-Stage Fuzzy Location Problems Under VaR Criterion With Irregular Fuzzy Variables |
| title_sort | note on two stage fuzzy location problems under var criterion with irregular fuzzy variables |
| topic | Discrete fuzzy variable facility location problem trapezoidal fuzzy number two-stage fuzzy programming value-at-risk |
| url | https://ieeexplore.ieee.org/document/9115014/ |
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