Title: Tableau form of the fuzzy primal-dual simplex algorithm for solving linear programmes with trapezoidal fuzzy numbers

Authors: Ali Ebrahimnejad

Addresses: Department of Mathematics, Qaemshahr Branch, Islamic Azad University, P.O. Box 163, Qaemshahr, Iran

Abstract: Recently, Ebrahimnejad (2011) generalised the primal-dual simplex algorithm for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems. In this paper, we describe the fuzzy primal-dual algorithm in tableau form and illustrate our approach by a numerical example. If there is no uncertainty among parameters then the proposed approach gives the same result as in crisp FLP problems. Since the proposed method is a direct extension of classical method so it is very easy to understand and apply the proposed method to find the fuzzy optimal solution of FLP problems occurring in the real life situations.

Keywords: fuzzy linear programming; FLP; fuzzy arithmetic; linear ranking functions; primal-dual simplex algorithm; fuzzy logic; trapezoidal fuzzy numbers.

DOI: 10.1504/IJOR.2013.056099

International Journal of Operational Research, 2013 Vol.18 No.2, pp.123 - 139

Available online: 13 Aug 2013 *

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