Solving minimum cost flow problem with fuzzy costs based on extension principle

In this paper, we propose a new method for solving minimum cost flow problem with fuzzy costs, which its aim is to find the least fuzzy cost of a commodity through a capacitated network in order to satisfy demands at certain nodes using available supplies at other nodes. Here, we use the concept of extension principle instead of using ranking functions which is so convenient to solve these problems. By using the proposed method, the optimal solution of minimum cost flow problems with fuzzy costs can be easily obtained. To illustrate the proposed method a numerical example is solved and the obtained results are discussed.