Application of fuzzy minimum cost flow problems to network design under uncertainty
Fuzzy Sets and Systems
Maximum cut in fuzzy nature: Models and algorithms
Journal of Computational and Applied Mathematics
IEEE Transactions on Fuzzy Systems
An algorithm for solving fuzzy maximal flow problems using generalized triangular fuzzy numbers
International Journal of Hybrid Intelligent Systems - Rough and Fuzzy Methods for Data Mining
Fuzzy Linear Programming Approach for Solving Fuzzy Transportation Problems with Transshipment
Journal of Mathematical Modelling and Algorithms
Fuzzy optimal solution of fuzzy transportation problems with transshipments
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
Models and algorithm of maximum flow problem in uncertain network
AICI'11 Proceedings of the Third international conference on Artificial intelligence and computational intelligence - Volume Part I
A biologically inspired solution for fuzzy shortest path problems
Applied Soft Computing
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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Network flow problems cover a wide range of engineering and management applications. Many streamlined solution methods have been devised for solving different types of the problems. This paper investigates the network flow problems in that the arc lengths of the network are fuzzy numbers. Based on the integer-solution property of the network flow problem, the Yager ranking indices can be calculated for the fuzzy arcs to change the fuzzy formulation of the problem to a crisp formulation. Consequently, the conventional streamlined solution methods can still be applied to find an optimal solution. This optimal solution is proved to be the same as that derived from an exhaustive comparison of all possible solutions. Two examples, one shortest path and one transshipment, discussed in some previous studies illustrate that the method proposed in this paper is able to find the optimal solution. To show that the proposed method is useful in solving real-world problems, the problem of multimedia transmission over the Internet is exemplified.