Application of fuzzy minimum cost flow problems to network design under uncertainty

This paper deals with fuzzy quantities and relations in multi-objective minimum cost flow problem. When t-norms and t-conorms are available, the goal programming is applied to minimize the deviation among the multiple costs of fuzzy flows and the given targets when the fuzzy supplies and demands are satisfied. To obtain the most optimistic and the most pessimistic satisficing solutions of this problem, two polynomial time algorithms are introduced applying some network transformations. To demonstrate the performance of this approach in actual substances, network design under fuzziness is considered and an efficient scheme is proposed including genetic algorithm together with fuzzy minimum cost flow problem. This scheme is applied on a pilot network for more description.