Ebrahimnejad, A. Some new results in linear programs with trapezoidal fuzzy numbers: finite convergence of the Ganesan and Veeramani’s method and a fuzzy revised simplex method. (English) Zbl 1225.90165 Appl. Math. Modelling 35, No. 9, 4526-4540 (2011). Summary: In a recent paper, K. Ganesan and P. Veeramani [Ann. Oper. Res. 143, 305–315 (2006; Zbl 1101.90091)] considered a kind of linear programming involving symmetric trapezoidal fuzzy numbers without converting them to the crisp linear programming problems and then proved fuzzy analogues of some important theorems of linear programming that lead to a new method for solving fuzzy linear programming (FLP) problems. In this paper, we obtain some another new results for FLP problems. In fact, we show that if an FLP problem has a fuzzy feasible solution, it also has a fuzzy basic feasible solution and if an FLP problem has an optimal fuzzy solution, it has an optimal fuzzy basic solution too. We also prove that in the absence of degeneracy, the method proposed by Ganesan and Veermani stops in a finite number of iterations. Then, we propose a revised kind of their method that is more efficient and robust in practice. Finally, we give a new method to obtain an initial fuzzy basic feasible solution for solving FLP problems. Cited in 11 Documents MSC: 90C70 Fuzzy and other nonstochastic uncertainty mathematical programming 90C05 Linear programming 90C49 Extreme-point and pivoting methods Keywords:fuzzy linear programming; fuzzy primal simplex algorithm; ranking; trapezoidal fuzzy number Citations:Zbl 1101.90091 PDFBibTeX XMLCite \textit{A. Ebrahimnejad}, Appl. Math. Modelling 35, No. 9, 4526--4540 (2011; Zbl 1225.90165) Full Text: DOI References: [1] Tanaka, H.; Okuda, T.; Asai, K., On fuzzy mathematical programming, J. Cybernet., 3, 37-46 (1974) · Zbl 0297.90098 [2] Belman, R. E.; Zadeh, L. A., Decision making in a fuzzy environment, Manage. 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