In this paper, a fuzzy fractional two-stage transshipment problem where all the parameters are represented by fuzzy numbers is studied. The problem uses the ratio of costs divided by benefits as the objective function. A solution method which employs the extension principle is used to find the fuzzy objective value of the problem. For this purpose, the fuzzy fractional two-stage transshipment problem is decomposed into two sub-problems where each of them is tackled individually using various \(\alpha\) levels to obtain the fuzzy objective function value and its associated membership function. To deal with the nonlinearity of the objective function the Charnes–Cooper transformation method is embedded to the proposed approach. The superior efficiency of the presented formulation and the proposed solution method is examined over a numerical example as well as a case study comparing to the literature.

本文研究了模糊分数两阶段转运问题，其中所有参数均由模糊数表示。该问题使用成本除以收益之比作为目标函数。采用扩展原理的求解方法被用于寻找问题的模糊目标值。为此，将模糊分数两阶段转运问题分解为两个子问题，其中每个子问题都使用各种\（\ alpha \）分别解决。以获得模糊目标函数值及其关联的隶属函数。为了处理目标函数的非线性，将Charnes-Cooper变换方法嵌入到所提出的方法中。通过数值示例以及与文献比较的案例研究，对所提出的配方和所提出的解决方法的卓越效率进行了研究。