In this paper, we reformulate the conventional DEA models as an imprecise DEA problem and propose a novel method for evaluating the DMUs when the inputs and outputs are fuzzy and/or ordinal or vary in intervals. For this purpose, we convert all data into interval data. In order to convert each fuzzy number into interval data, we use the nearest weighted interval approximation of fuzzy numbers by applying the weighting function, and we convert each ordinal data into interval one. In this manner, we could convert all data into interval data. The presented models determine the interval efficiencies for DMUs. To rank DMUs based on their associated interval efficiencies, we first apply the Ω-index that is developed for ranking of interval numbers. Then, by introducing an ideal DMU, we rank efficient DMUs to present a complete ranking. Finally, we use one example to illustrate the process and one real application in health care to show the usefulness of the proposed approach. For this evaluation, we consider interval, ordinal, and fuzzy data alongside the precise data to evaluate 38 hospitals selected by OIG. The results reveal the capabilities of the presented method to deal with the imprecise data.

中文翻译：

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序数和区间数据的模糊数据包络分析

在本文中，我们将传统的 DEA 模型重新表述为不精确的 DEA 问题，并提出了一种在输入和输出模糊和/或有序或间隔变化时评估 DMU 的新方法。为此，我们将所有数据转换为区间数据。为了将每个模糊数转换为区间数据，我们通过应用加权函数使用模糊数的最近加权区间近似，并将每个序数数据转换为区间一。通过这种方式，我们可以将所有数据转换为区间数据。提出的模型确定了 DMU 的区间效率。为了根据相关的区间效率对 DMU 进行排名，我们首先应用Ω- 为区间数排序而开发的索引。然后，通过引入一个理想的 DMU，我们对有效的 DMU 进行排名，以呈现完整的排名。最后，我们用一个例子来说明这个过程和一个在医疗保健中的实际应用，以展示所提出的方法的有用性。在本次评估中，我们考虑了区间、序数和模糊数据以及精确数据，以评估 OIG 选择的 38 家医院。结果揭示了所提出的方法处理不精确数据的能力。