This paper presents a new approach to the solution of resource or task allocation problems. A network flow optimization problem is posed that combines binary integer programming methods with fuzzy decision making processes, to obtain optimal solutions to resource allocation problems. In existing resource allocation methods there is a large burden on accurately specifying cost functions associated with tasks that are carried out as flows on arcs through the network. Fuzzy decision theory is utilized to model these objective functions, in order to capture imprecise conditions associated with decision making under constraint feedback information. Efficient programming methods are used to obtain solution sets of optimal binary decision variables.