An Interactive Approach for Solving the Multiobjective Minimum Cost Flow Problem in the Fuzzy Environment
This paper deals with the multiobjective minimum cost flow (F-MOMCF) with fuzzy penalty characterized by trapezoidal fuzzy numbers. Through the use of α-cut, the F-MOMCF problem is transformed into the α-MOMCF problem. The α-MOMCF problem can be solved using an interactive approach combined with the...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/6247423 |
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| author | Majed G. Alharbi Hamiden Abd El-Wahed Khalifa E. E. Ammar |
| author_facet | Majed G. Alharbi Hamiden Abd El-Wahed Khalifa E. E. Ammar |
| author_sort | Majed G. Alharbi |
| collection | DOAJ |
| description | This paper deals with the multiobjective minimum cost flow (F-MOMCF) with fuzzy penalty characterized by trapezoidal fuzzy numbers. Through the use of α-cut, the F-MOMCF problem is transformed into the α-MOMCF problem. The α-MOMCF problem can be solved using an interactive approach combined with the weighting Tchebycheff problem. The advantages of this method are that it elicits information from the decision maker (DM) to modify the given constraint set, it gives the optimum penalty, and the effort required for obtaining the solution is reduced. The stability set of the first kind related to the α-best compromise solution is determined. A numerical example is given for illustration and to check the validity of the approach. |
| format | Article |
| id | doaj-art-b49dde8917fd43b8b2d147b3023c5f1e |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-b49dde8917fd43b8b2d147b3023c5f1e2025-02-03T01:01:24ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/62474236247423An Interactive Approach for Solving the Multiobjective Minimum Cost Flow Problem in the Fuzzy EnvironmentMajed G. Alharbi0Hamiden Abd El-Wahed Khalifa1E. E. Ammar2Department of Mathematics, College of Arts and Sciences, Methnab, Qassim University, Buridah, Saudi ArabiaOperations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, EgyptMathematics Department, Faculty of Science, Tanta University, Tanta, EgyptThis paper deals with the multiobjective minimum cost flow (F-MOMCF) with fuzzy penalty characterized by trapezoidal fuzzy numbers. Through the use of α-cut, the F-MOMCF problem is transformed into the α-MOMCF problem. The α-MOMCF problem can be solved using an interactive approach combined with the weighting Tchebycheff problem. The advantages of this method are that it elicits information from the decision maker (DM) to modify the given constraint set, it gives the optimum penalty, and the effort required for obtaining the solution is reduced. The stability set of the first kind related to the α-best compromise solution is determined. A numerical example is given for illustration and to check the validity of the approach.http://dx.doi.org/10.1155/2020/6247423 |
| spellingShingle | Majed G. Alharbi Hamiden Abd El-Wahed Khalifa E. E. Ammar An Interactive Approach for Solving the Multiobjective Minimum Cost Flow Problem in the Fuzzy Environment Journal of Mathematics |
| title | An Interactive Approach for Solving the Multiobjective Minimum Cost Flow Problem in the Fuzzy Environment |
| title_full | An Interactive Approach for Solving the Multiobjective Minimum Cost Flow Problem in the Fuzzy Environment |
| title_fullStr | An Interactive Approach for Solving the Multiobjective Minimum Cost Flow Problem in the Fuzzy Environment |
| title_full_unstemmed | An Interactive Approach for Solving the Multiobjective Minimum Cost Flow Problem in the Fuzzy Environment |
| title_short | An Interactive Approach for Solving the Multiobjective Minimum Cost Flow Problem in the Fuzzy Environment |
| title_sort | interactive approach for solving the multiobjective minimum cost flow problem in the fuzzy environment |
| url | http://dx.doi.org/10.1155/2020/6247423 |
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