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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

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.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C05 Linear programming
90C49 Extreme-point and pivoting methods

Citations:

Zbl 1101.90091
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References:

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