Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Linear programming with fuzzy variables
Fuzzy Sets and Systems
Fully fuzzified linear programming, solution and duality
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Ranking function-based solutions of fully fuzzified minimal cost flow problem
Information Sciences: an International Journal
Network flow problems with fuzzy arc lengths
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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In this paper, we generalize the bounded dual simplex algorithm for solving minimum cost flow problem with fuzzy cost, 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. This algorithm begins with dual feasibility and iterates between dual and primal problems until optimality is achieved. Here, we use the linear ranking functions to compare fuzzy numbers. 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.