An algorithm for the fuzzy maximum flow problem

The problem of finding the maximum flow between a source and a destination node in a network with uncertainties in its capacities is an important problem of network flows, since it has a wide range of applications in different areas (telecommunications, transportations, manufacturing, etc) and therefore deserves special attention. However, due to complexity in working with this kind of problems, there are a few algorithms in literature, which demand that the user informs the desirable maximum flow, which is difficult when the network is the large scale. In this paper, an algorithm based on the classic algorithm of Ford-Fulkerson is proposed. The algorithm uses the technique of the incremental graph and it does not request that the decision-maker informs the desirable flow, in contrast of the main works of literature. The uncertainties of the parameters are resolved using the fuzzy sets theory.