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首页> 外文期刊>Applied Mathematical Modelling >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
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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

机译：具有梯形模糊数的线性程序的一些新结果：Ganesan和Veeramani方法的有限收敛性以及模糊修正单纯形法

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摘要

In a recent paper, Ganesan and Veermani [K. Ganesan, P. Veeramani, Fuzzy linear programs with trapezoidal fuzzy numbers, Ann. Oper. Res. 143 (2006) 305-315] 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.
机译：在最近的一篇论文中，Ganesan和Veermani [K. Ganesan，P。Veeramani，带有梯形模糊数的模糊线性程序，Ann。歌剧Res。 143（2006）305-315]考虑了一种包含对称梯形模糊数的线性规划，而没有将它们转换为清晰的线性规划问题，然后证明了线性规划的一些重要定理的模糊类似物，从而产生了一种解决模糊线性规划的新方法编程（FLP）问题。在本文中，我们针对FLP问题获得了另一个新结果。实际上，我们表明，如果FLP问题具有模糊可行解，则它也具有模糊基本可行解；如果FLP问题具有最优模糊解，则也具有最优模糊基本解。我们还证明，在不存在简并性的情况下，Ganesan和Veermani提出的方法在有限的迭代中停止。然后，我们提出一种改进的方法，在实践中更加有效和可靠。最后，我们给出了一种新的方法来获得初始模糊基本可行解，以解决FLP问题。

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