New Concepts of Feasibility and Efficiency of Solutions in Fuzzy Mathematical Programming Problems
Some new concepts in regards to ᾱ-feasibility and ᾱ-efficiency of solutions in fuzzy mathematical programming problems are introduced in this paper, where ᾱ is a vector of distinct satisfaction degrees. Based on the defined concepts, a new method is suggested to solve fuzzy mathematical programmi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Tsinghua University Press
2014-06-01
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| Series: | Fuzzy Information and Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1616865814000259 |
| _version_ | 1827847080125661184 |
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| author | H. Attari S.H. Nasseri |
| author_facet | H. Attari S.H. Nasseri |
| author_sort | H. Attari |
| collection | DOAJ |
| description | Some new concepts in regards to ᾱ-feasibility and ᾱ-efficiency of solutions in fuzzy mathematical programming problems are introduced in this paper, where ᾱ is a vector of distinct satisfaction degrees. Based on the defined concepts, a new method is suggested to solve fuzzy mathematical programming problems. In this sense, the proposed approach enables decision makers to take into account more flexible solutions by allowing desired distinct satisfactions in constraints. In the case of linear problems with fuzzy constraints, multi-parametric programming is employed to obtain the optimal solution as an affine function of distinct satisfaction degrees. In particular, it proves that the obtained solution is convex and continuous. Therefore, the different optimal solutions can be obtained by a simple substituting the new values of satisfaction parameters into the parametric profiles without any further optimization calculations, which is desirable for online optimization and sensitivity analysis of the profit to satisfaction parameters. |
| first_indexed | 2024-03-12T09:25:48Z |
| format | Article |
| id | doaj.art-e429cd9a36864baeb1c5d2f724eb23ba |
| institution | Directory Open Access Journal |
| issn | 1616-8658 |
| language | English |
| last_indexed | 2024-03-12T09:25:48Z |
| publishDate | 2014-06-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | Fuzzy Information and Engineering |
| spelling | doaj.art-e429cd9a36864baeb1c5d2f724eb23ba2023-09-02T14:16:53ZengTsinghua University PressFuzzy Information and Engineering1616-86582014-06-016220322110.1016/j.fiae.2014.08.005New Concepts of Feasibility and Efficiency of Solutions in Fuzzy Mathematical Programming ProblemsH. AttariS.H. NasseriSome new concepts in regards to ᾱ-feasibility and ᾱ-efficiency of solutions in fuzzy mathematical programming problems are introduced in this paper, where ᾱ is a vector of distinct satisfaction degrees. Based on the defined concepts, a new method is suggested to solve fuzzy mathematical programming problems. In this sense, the proposed approach enables decision makers to take into account more flexible solutions by allowing desired distinct satisfactions in constraints. In the case of linear problems with fuzzy constraints, multi-parametric programming is employed to obtain the optimal solution as an affine function of distinct satisfaction degrees. In particular, it proves that the obtained solution is convex and continuous. Therefore, the different optimal solutions can be obtained by a simple substituting the new values of satisfaction parameters into the parametric profiles without any further optimization calculations, which is desirable for online optimization and sensitivity analysis of the profit to satisfaction parameters.http://www.sciencedirect.com/science/article/pii/S1616865814000259Feasibility and efficiency of solutionsFuzzy linear programmingMulti-parametric programmingSensitivity analysis |
| spellingShingle | H. Attari S.H. Nasseri New Concepts of Feasibility and Efficiency of Solutions in Fuzzy Mathematical Programming Problems Fuzzy Information and Engineering Feasibility and efficiency of solutions Fuzzy linear programming Multi-parametric programming Sensitivity analysis |
| title | New Concepts of Feasibility and Efficiency of Solutions in Fuzzy Mathematical Programming Problems |
| title_full | New Concepts of Feasibility and Efficiency of Solutions in Fuzzy Mathematical Programming Problems |
| title_fullStr | New Concepts of Feasibility and Efficiency of Solutions in Fuzzy Mathematical Programming Problems |
| title_full_unstemmed | New Concepts of Feasibility and Efficiency of Solutions in Fuzzy Mathematical Programming Problems |
| title_short | New Concepts of Feasibility and Efficiency of Solutions in Fuzzy Mathematical Programming Problems |
| title_sort | new concepts of feasibility and efficiency of solutions in fuzzy mathematical programming problems |
| topic | Feasibility and efficiency of solutions Fuzzy linear programming Multi-parametric programming Sensitivity analysis |
| url | http://www.sciencedirect.com/science/article/pii/S1616865814000259 |
| work_keys_str_mv | AT hattari newconceptsoffeasibilityandefficiencyofsolutionsinfuzzymathematicalprogrammingproblems AT shnasseri newconceptsoffeasibilityandefficiencyofsolutionsinfuzzymathematicalprogrammingproblems |