Evaluating efficiency according to the different states of returns to scale (RTS) is crucial to resource allocation and scientific decision for decision-making units (DMUs), but this kind of evaluation will become very difficult when the DMUs are in an uncertain random environment. In this paper, we attempt to explore the uncertain random data envelopment analysis approach so as to solve the problem that the inputs and outputs of DMUs are uncertain random variables. Chance theory is applied to handling the uncertain random variables, and hence, two evaluating models, one for increasing returns to scale (IRS) and the other for decreasing returns to scale (DRS), are proposed, respectively. Along with converting the two uncertain random models into corresponding equivalent forms, we also provide a numerical example to illustrate the evaluation results of these models.

中文翻译：

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不确定的随机数据包络分析：规模收益的效率估计

根据规模收益率（RTS）的不同状态评估效率对于决策单位（DMU）的资源分配和科学决策至关重要，但是当DMU处于不确定的随机环境中时，这种评估将变得非常困难。本文尝试探索不确定的随机数据包络分析方法，以解决DMU的输入和输出是不确定的随机变量的问题。应用机会理论处理不确定的随机变量，因此，分别提出了两种评估模型，一种用于增加规模收益（IRS），另一种用于减少规模收益（DRS）。除了将两个不确定的随机模型转换为相应的等效形式之外，