TY - JOUR
T1 - Network Flow Problems with Fuzzy Arc Lengths
AU - Liu, Shiang Tai
AU - Kao, Chiang
N1 - Funding Information:
Manuscript received May 28, 2000; revised December 27, 2000 and November 5, 2001. This work was supported by the National Science Council of the R.O.C. under Contract NSC89-2416-H006-020. This paper was recommended by Associate Editor W. Scherer.
PY - 2004/2
Y1 - 2004/2
N2 - 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.
AB - 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.
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U2 - 10.1109/TSMCB.2003.818560
DO - 10.1109/TSMCB.2003.818560
M3 - Article
C2 - 15369120
AN - SCOPUS:0742272543
SN - 1083-4419
VL - 34
SP - 765
EP - 769
JO - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
JF - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IS - 1
ER -