Linear programmes with trapezoidal fuzzy numbers: a duality approach

Solving fuzzy linear programming problems have received a great deal of attention. Recently, Ganesan and Veeramani (2006) developed a new method for solving a kind of these problems involving symmetric trapezoidal fuzzy numbers without converting them to the crisp linear programming problems based on primal simplex method. But their method has no efficient when a primal basic feasible solution is not at hand. In this paper, we develop a new dual simplex algorithm to overcome this shortcoming by using the duality results which has been proposed by Nasseri and Mahdavi‐Amiri (2009) and Nasseri et al. (2010). This algorithm starts with a dual basic feasible solution, but primal basic infeasible solution and walks to an optimal solution by moving among adjacent dual basic feasible solution.