Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function
Recently, various methods have been developed for solving linear programming problems with fuzzy number, such as simplex method and dual simplex method. But their computational complexities are exponential, which is not satisfactory for solving large-scale fuzzy linear programming problems, especial...
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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/10.1155/2013/795098 |
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| author | Yi-hua Zhong Yan-lin Jia Dandan Chen Yan Yang |
| author_facet | Yi-hua Zhong Yan-lin Jia Dandan Chen Yan Yang |
| author_sort | Yi-hua Zhong |
| collection | DOAJ |
| description | Recently, various methods have been developed for solving linear programming problems with fuzzy number, such as simplex method and dual simplex method. But their computational complexities are exponential, which is not satisfactory for solving large-scale fuzzy linear programming problems, especially in the engineering field. A new method which can solve large-scale fuzzy number linear programming problems is presented in this paper, which is named a revised interior point method. Its idea is similar to that of interior point method used for solving linear programming problems in crisp environment before, but its feasible direction and step size are chosen by using trapezoidal fuzzy numbers, linear ranking function, fuzzy vector, and their operations, and its end condition is involved in linear ranking function. Their correctness and rationality are proved. Moreover, choice of the initial interior point and some factors influencing the results of this method are also discussed and analyzed. The result of algorithm analysis and example study that shows proper safety factor parameter, accuracy parameter, and initial interior point of this method may reduce iterations and they can be selected easily according to the actual needs. Finally, the method proposed in this paper is an alternative method for solving fuzzy number linear programming problems. |
| format | Article |
| id | doaj-art-5e399cda828d4dd4a6fc732f4847d270 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5e399cda828d4dd4a6fc732f4847d2702025-08-20T02:06:03ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/795098795098Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking FunctionYi-hua Zhong0Yan-lin Jia1Dandan Chen2Yan Yang3School of Science, Southwest Petroleum University, Chengdu, Sichuan 610500, ChinaSchool of Science, Southwest Petroleum University, Chengdu, Sichuan 610500, ChinaSchool of Science, Southwest Petroleum University, Chengdu, Sichuan 610500, ChinaSchool of Science, Southwest Petroleum University, Chengdu, Sichuan 610500, ChinaRecently, various methods have been developed for solving linear programming problems with fuzzy number, such as simplex method and dual simplex method. But their computational complexities are exponential, which is not satisfactory for solving large-scale fuzzy linear programming problems, especially in the engineering field. A new method which can solve large-scale fuzzy number linear programming problems is presented in this paper, which is named a revised interior point method. Its idea is similar to that of interior point method used for solving linear programming problems in crisp environment before, but its feasible direction and step size are chosen by using trapezoidal fuzzy numbers, linear ranking function, fuzzy vector, and their operations, and its end condition is involved in linear ranking function. Their correctness and rationality are proved. Moreover, choice of the initial interior point and some factors influencing the results of this method are also discussed and analyzed. The result of algorithm analysis and example study that shows proper safety factor parameter, accuracy parameter, and initial interior point of this method may reduce iterations and they can be selected easily according to the actual needs. Finally, the method proposed in this paper is an alternative method for solving fuzzy number linear programming problems.http://dx.doi.org/10.1155/2013/795098 |
| spellingShingle | Yi-hua Zhong Yan-lin Jia Dandan Chen Yan Yang Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function Journal of Applied Mathematics |
| title | Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function |
| title_full | Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function |
| title_fullStr | Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function |
| title_full_unstemmed | Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function |
| title_short | Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function |
| title_sort | interior point method for solving fuzzy number linear programming problems using linear ranking function |
| url | http://dx.doi.org/10.1155/2013/795098 |
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