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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| Published in: | Journal of mathematics (Hidawi) Vol. 2020; no. 2020; pp. 1 - 7 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Cairo, Egypt
Hindawi Publishing Corporation
2020
Hindawi John Wiley & Sons, Inc Wiley |
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| ISSN: | 2314-4629, 2314-4785 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Khalifa, Hamiden Abd El-Wahed Alharbi, Majed G. Ammar, E. E. |
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| Copyright | Copyright © 2020 Majed G. Alharbi et al. Copyright © 2020 Majed G. Alharbi et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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| SubjectTerms | Algorithms Decision making Fuzzy logic Fuzzy sets Inventory Linear programming Mathematical programming Mathematics Minimum cost Network management systems Optimization |
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| Title | An Interactive Approach for Solving the Multiobjective Minimum Cost Flow Problem in the Fuzzy Environment |
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