N. Mahdavi-Amiri and S. H. Nasseri, “Duality Results and a Dual Simplex Method for Linear Programming Problems with Trapezoidal Fuzzy Variables,” Fuzzy Sets and Systems, Vol. 158, No. 17, 2007, pp. 1961-1978. doi:10.1016/j.fss.2007.05.005

has been cited by the following article:

• TITLE: A Primal-Dual Simplex Algorithm for Solving Linear Programming Problems with Symmetric Trapezoidal Fuzzy Numbers

  AUTHORS: Ali Ebrahimnejad

  KEYWORDS: Fuzzy Linear Programming, Fuzzy Arithmetic, Fuzzy Orders, Primal-Dual Simplex Algorithm

  JOURNAL NAME: Applied Mathematics, Vol.2 No.6, June 21, 2011

  ABSTRACT: Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach.