In this paper, we have proposed a mathematical formulation of fuzzy minimum cost flow problem for damageable items transportation. For the imprecise model, capacity, cost, percentage of unit damage of each route have been considered as triangular fuzzy numbers. This problem has been solved by using the k-preference integration method, the area compensation method, and the signed distance method. Finally, to show the validity of the proposed model, a numerical example is provided and solved with Wolfram Mathematica 9.
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