Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming
In the current literatures, there are several models of fully fuzzy linear programming (FFLP) problems where all the parameters and variables were fuzzy numbers but the constraints were crisp equality or inequality. In this paper, an FFLP problem with fuzzy equality constraints is discussed, and a m...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/726296 |
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| _version_ | 1832545819983609856 |
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| author | Haifang Cheng Weilai Huang Jianhu Cai |
| author_facet | Haifang Cheng Weilai Huang Jianhu Cai |
| author_sort | Haifang Cheng |
| collection | DOAJ |
| description | In the current literatures, there are several models of fully fuzzy linear programming (FFLP) problems where all the parameters and variables were fuzzy numbers but the constraints were crisp equality or inequality. In this paper, an FFLP problem with fuzzy equality constraints is discussed, and a method for solving this FFLP problem is also proposed. We first transform the fuzzy equality constraints into the crisp inequality ones using the measure of the similarity, which is interpreted as the feasibility degree of constrains, and then transform the fuzzy objective into two crisp objectives by considering expected value and uncertainty of fuzzy objective. Since the feasibility degree of constrains is in conflict with the optimal value of objective function, we finally construct an auxiliary three-objective linear programming problem, which is solved through a compromise programming approach, to solve the initial FFLP problem. To illustrate the proposed method, two numerical examples are solved. |
| format | Article |
| id | doaj-art-e82f4b18fbe040308037383fbfd1347d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e82f4b18fbe040308037383fbfd1347d2025-02-03T07:24:46ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/726296726296Solving a Fully Fuzzy Linear Programming Problem through Compromise ProgrammingHaifang Cheng0Weilai Huang1Jianhu Cai2School of Management, Huazhong University of Science and Technology, Wuhan 430074, ChinaSchool of Management, Huazhong University of Science and Technology, Wuhan 430074, ChinaCollege of Economics and Management, Zhejiang University of Technology, Hangzhou 310023, ChinaIn the current literatures, there are several models of fully fuzzy linear programming (FFLP) problems where all the parameters and variables were fuzzy numbers but the constraints were crisp equality or inequality. In this paper, an FFLP problem with fuzzy equality constraints is discussed, and a method for solving this FFLP problem is also proposed. We first transform the fuzzy equality constraints into the crisp inequality ones using the measure of the similarity, which is interpreted as the feasibility degree of constrains, and then transform the fuzzy objective into two crisp objectives by considering expected value and uncertainty of fuzzy objective. Since the feasibility degree of constrains is in conflict with the optimal value of objective function, we finally construct an auxiliary three-objective linear programming problem, which is solved through a compromise programming approach, to solve the initial FFLP problem. To illustrate the proposed method, two numerical examples are solved.http://dx.doi.org/10.1155/2013/726296 |
| spellingShingle | Haifang Cheng Weilai Huang Jianhu Cai Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming Journal of Applied Mathematics |
| title | Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming |
| title_full | Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming |
| title_fullStr | Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming |
| title_full_unstemmed | Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming |
| title_short | Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming |
| title_sort | solving a fully fuzzy linear programming problem through compromise programming |
| url | http://dx.doi.org/10.1155/2013/726296 |
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