To solve a fuzzy linear program, we need to compare fuzzy numbers. Here, we make use of our recently proposed modified Kerre's method for comparison of LR fuzzy numbers. We give some new results on LR fuzzy numbers and show that to compare two LR fuzzy numbers, it is not necessary to compute the fuzzy maximum of two numbers directly. Using the modified Kerre's method, we propose a new variable neighborhood search algorithm for solving fuzzy number linear programming problems. In our algorithm, the local search is defined based on descent directions, which are found by solving four crisp mathematical programming problems. In several methods, a fuzzy optimization problem is converted to a crisp problem but in our proposed method, using our modified Kerre's method, the fuzzy optimization problem is solved directly, without changing it to a crisp program. We provide examples to compare the performance of our proposed algorithm to other available methods. We show the effectiveness of our proposed algorithm by using the nonparametric statistical sign test.

中文翻译：

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修正Kerre法求解模糊数线性规划问题的变邻域搜索算法


为了求解模糊线性程序，我们需要比较模糊数。在这里，我们利用最近提出的改进的 Kerre 方法来比较 LR 模糊数。我们给出了一些关于 LR 模糊数的新结果，并表明要比较两个 LR 模糊数，不需要直接计算两个数的模糊最大值。使用改进的 Kerre 方法，我们提出了一种新的变邻域搜索算法来解决模糊数线性规划问题。在我们的算法中，局部搜索是基于下降方向定义的，下降方向是通过解决四个清晰的数学规划问题找到的。在几种方法中，模糊优化问题被转换为清晰问题，但在我们提出的方法中，使用我们修改的 Kerre 方法，直接求解模糊优化问题，而不将其更改为清晰程序。我们提供示例来比较我们提出的算法与其他可用方法的性能。我们通过使用非参数统计符号检验来展示我们提出的算法的有效性。