Title: Linear programmes with trapezoidal fuzzy numbers: a duality approach

Authors: Ali Ebrahimnejad; S.H. Nasseri

Addresses: Department of Mathematics, Islamic Azad University, Qaemshahr Branch, P.O. Box 163, Qaemshahr, Iran ' Department of Mathematics, Faculty of Sciences, Mazandaran University, Babolsar, Iran

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.

Keywords: FLP; fuzzy linear programming; duality; dual simplex algorithm; symmetric trapezoidal fuzzy numbers.

DOI: 10.1504/IJOR.2012.044028

International Journal of Operational Research, 2012 Vol.13 No.1, pp.67 - 89

Published online: 11 Jan 2015 *

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