This paper considers a generalized fuzzy version of maximum flow problem in which arc capacities are fuzzy variables. The problem is to find a maximum flow under some chance constraints with respect to credibility measure of arc flow of network. Some crisp equivalents of fuzzy chance constraints are presented when the fuzzy capacities are characterized by trapezoidal fuzzy numbers and general fuzzy numbers respectively. Furthermore, a genetic algorithm is used to solve the maximum flow with these crisp equivalents. Finally, a numerical example is provided for the effectiveness of the model and algorithm.
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