The present paper proposes a number of models for calculating the average efficiency of two-stage networks using DEA and DEA-R with fuzzy data. If the input, intermediate, and output parameters are available in a two-stage network, DEA and DEA-R models can be used to compute the efficiency. When evaluating decision-making units (DMUs) in two-stage network DEA, the respective programming models are fractional. Meanwhile, in DEA-R, the proposed programming models are linear. Although, it is necessary that the output-to-input ratios (output-orientation) or vice versa (input orientation) be defined and available. Furthermore, DEA-R models can also evaluate DMUs with a network structure when only ratio data are available. Generally, using fuzzy data is necessary for an accurate evaluation of organizations with a two-stage network structure. Therefore, in the present article, using the α-cut approach, an average efficiency model is proposed for the first and second stages of a network structure. At the end, a comparison is made between the mean efficiency scores of a number of airlines by considering fuzzy data in two-stage network DEA and DEA-R.

中文翻译：

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基于DEA和DEA-R模糊数据的平均效率两阶段网络评估

本文提出了许多使用模糊数据的DEA和DEA-R计算两阶段网络平均效率的模型。如果输入，中间和输出参数在两阶段网络中可用，则可以使用DEA和DEA-R模型来计算效率。在评估两阶段网络DEA中的决策单元（DMU）时，各个编程模型都是分数。同时，在DEA-R中，所提出的编程模型是线性的。但是，必须定义并提供输出与输入之比（输出方向），反之亦然（输入方向）。此外，当仅比率数据可用时，DEA-R模型还可以评估具有网络结构的DMU。通常，使用模糊数据对于具有两阶段网络结构的组织的准确评估是必要的。因此，在本文中，使用α割方法，针对网络结构的第一阶段和第二阶段提出了平均效率模型。最后，通过考虑两级网络DEA和DEA-R中的模糊数据，比较了多家航空公司的平均效率得分。