Data envelopment analysis (DEA) is a popular mathematical tool for analyzing the relative efficiency of homogenous decision-making units (DMUs). However, the existing DEA models cannot tackle the newly confronted applications with imprecise and negative data as well as undesirable outputs simultaneously. Thus, we introduce undesirable outputs into modified slack-based measure (MSBM) model and propose an interval-modified slack-based measure (IMSBM) model, which extends the application of interval DEA (IDEA) in fields that concern with less undesirable outputs. The novelties of the model are that it considers the undesirable outputs while dealing with imprecise and negative data, and it is slack-based. Furthermore, the model with undesirable outputs is proven translation-invariant and unit-invariant. Moreover, a numerical example is provided to illustrate the changes of the lower and upper bounds of the efficiency score after considering the undesirable outputs. The empirical results show that, without considering undesirable outputs, most of the lower bounds of the efficiency scores will be overestimated when the DMUs are weakly efficient and inefficient. The upper bound will also change after considering undesirable outputs when the DMU is inefficient. Finally, an improved degree of preference approach is introduced to rank the DMUs.

中文翻译：

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考虑不良输出时的DEA间隔效率测量

数据包络分析（DEA）是一种流行的数学工具，用于分析同质决策单元（DMU）的相对效率。但是，现有的DEA模型无法同时解决不精确和负面数据以及不良输出的新应用。因此，我们将不良输出引入到基于改进的基于松弛的度量（MSBM）模型中，并提出了一种基于间隔修正的基于松弛的度量（IMSBM）模型，该模型扩展了间隔DEA（IDEA）在涉及较少不良输出的领域中的应用。该模型的新颖之处在于，它在处理不精确和负面数据时会考虑不良输出，并且它是基于松弛的。此外，具有不期望的输出的模型被证明是平移不变的和单位不变的。此外，提供了一个数值示例来说明考虑不期望的输出后效率得分上下限的变化。实证结果表明，如果DMU效率低下和效率低下，则在不考虑不期望的输出的情况下，效率得分的大多数下限将被高估。当DMU效率低下时，在考虑不期望的输出后，上限也会发生变化。最后，引入了一种改进的优先级方法来对DMU进行排名。当DMU效率低下时，在考虑不期望的输出后，上限也会发生变化。最后，引入了一种改进的优先级方法来对DMU进行排名。当DMU效率低下时，在考虑不期望的输出后，上限也会发生变化。最后，引入了一种改进的优先级方法来对DMU进行排名。