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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Bibliographic Details
Published in:Journal of mathematics (Hidawi) Vol. 2020; no. 2020; pp. 1 - 7
Main Authors: Alharbi, Majed G., Ammar, E. E., Khalifa, Hamiden Abd El-Wahed
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Publishing Corporation 2020
Hindawi
John Wiley & Sons, Inc
Wiley
Subjects:
Algorithms
Decision making
Fuzzy logic
Fuzzy sets
Inventory
Linear programming
Mathematical programming
Mathematics
Minimum cost
Network management systems
Optimization
ISSN:2314-4629, 2314-4785
Online Access:Get full text
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Summary: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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ISSN:2314-4629
2314-4785
DOI:10.1155/2020/6247423