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Several authors have proposed different methods for solving fuzzy minimum cost flow (MCF) problems. In this paper, some single and multi-objective fuzzy MCF problems are chosen which cannot be solved by using any of the existing methods and a new method is proposed for solving such type of problems. The main advantage of the proposed method over existing methods is that the fuzzy MCF problems which can be solved by using the existing methods can also be solved by the proposed method. But, there exist several fuzzy MCF problems which can be solved only by using the proposed method i.e., it is not possible to solve these problems by using the existing methods. To illustrate the proposed method and also to show the advantages of the proposed method over existing methods some single and multi-objective fuzzy MCF problems which cannot be solved by using the existing methods are solved by using the proposed method and the obtained results are discussed. [ABSTRACT FROM AUTHOR]