Linear programmes with trapezoidal fuzzy numbers: a duality approach

Abstract

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.