We present, in this paper, a method for solving linear programming problems with fuzzy costs based on the classical method of decompositions Dantzig-Wolfe. Methods using decomposition techniques address problems that have a special structure in the set of constraints. An example of such a problem that has this structure is the fuzzy multicommodity flow problem. This problem can be modeled by a graph whose nodes represent points of supply, demand and passage of commodities, which travel on the arcs of the network. The objective is to determine the flow of each commodity on the arcs, in order to meet demand at minimal cost while respecting the capacity constraints of the arcs and the flow conservation constraints of the nodes. Using the theory of fuzzy sets, the proposed method aims to find the optimal solution, working with the problem in the fuzzy form during the resolution procedure. © 2012 Elsevier Ltd. All rights reserved.391233943407Bazaraa, M.S., Jarvis, J.J., Sherali, H.D., (2005) Linear Programming and Network Flows, , John Wiley & Sons New JerseyDubois, D., Prade, H., (1980) Fuzzy Sets and Systems: Theory and Applications, , Academic Press New YorkFord, L.R., Fulkerson, D.R., (1962) Flows in Networks, , Princeton University Press New JerseyGhatee, M., Hashemi, S.M., Some concepts of the fuzzy multicommodity flow problem and their application in fuzzy network design (2009) Mathematical and Computer Modelling, 49, pp. 1030-1043Hernandes, F., (2007) Algoritmos Para Problemas de Grafos Com Incertezas, , PhD thesis, FEEC, UNICAMP, Campinas, SPHernandes, F., Lamata, M.T., Verdegay, J.L., Yamakami, A., The shortest path problem on networks with fuzzy parameters (2007) Fuzzy Sets and Systems, 158 (14), pp. 1561-1570. , DOI 10.1016/j.fss.2007.02.022, PII S0165011407001066Hu, T.C., Multicommodity network flows (1962) Operations Research, 11, pp. 344-360Kaufmann, A., Gupta, M.M., (1988) Fuzzy Mathematical Models in Engineering and Management Science, , North Holland AmsterdamKlir, G., Yuan, B., (1995) Fuzzy Sets and Fuzzy Logic: Theory and Applications, , Prentice-Hall Upper Saddle River, NJOkada, S., Soper, T., A shortest path problem on a network with fuzzy arc lengths (2000) Fuzzy Sets and Systems, 109, pp. 129-140Okada, S., Fuzzy shortest path problems incorporating interactivity among paths (2004) Fuzzy Sets and Systems, 142 (3), pp. 335-357Pedrycz, W., Gomide, F., (2007) Fuzzy Systems Engineering Toward Human-centric Computing, , John Wiley and Sons Hoboken, NJTan, L.G., Sinclair, M.C., Wavelength assignment between the central nodes of the cost239 European optical network (1995) 11th UK Performance Engineering Workshop, pp. 235-247. , LiverpoolVerga, J., Ciappina, J.R., Yamakami, A., Algoritmo para a Resolução do Problema de Fluxo Multiproduto Fuzzy (2009) XLI Simpósio Brasileiro de Pesquisa Operacional, , Porto Seguro, BAZadeh, L., Fuzzy sets (1965) Journal of Information and Control, 8, pp. 338-353Zadeh, L., Fuzzy sets as a theory of possibility (1978) Journal of Fuzzy Sets and Systems, 1, pp. 3-28Zimmermann, H.-J., (1996) Fuzzy Set Theory - And Its Applications, , Kluwer Academic Publishers Boston