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Efficiencies of two-stage systems with fuzzy data

机译：具有模糊数据的两阶段系统的效率

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Two-stage DEA (data envelopment analysis) models show the performance of individual processes, and thus are more informative than the conventional one-stage models for making decisions. This paper extends this approach from deterministic to uncertain situations, where the observations are represented by fuzzy numbers. The extension principle is utilized to develop a pair of two-level mathematical programs to calculate the lower and upper bounds of the α-cut of the fuzzy efficiency. By enumerating various values of a, the membership functions of fuzzy efficiencies are constructed numerically. It is found that the property of the system efficiency being equal to the product of the two process efficiencies, which holds for the deterministic case, also holds for the fuzzy case. This property can be generalized to series systems with more than two processes. An example of non-life insurance companies in Taiwan is used to explain how to calculate the system and process efficiencies and how to derive their relationship when the data is fuzzy.
机译：两阶段DEA（数据包络分析）模型显示了各个流程的性能，因此比常规的一阶段模型进行决策时提供的信息更多。本文将这种方法从确定性情况扩展到不确定性情况，在这种情况下，观察值由模糊数表示。利用扩展原理开发了两个两级数学程序，以计算模糊效率的α-割的上下限。通过枚举a的各种值，数字地构造了模糊效率的隶属函数。发现系统效率等于两个过程效率的乘积，对于确定性情况成立，对于模糊情况也成立。该特性可以推广到具有两个以上过程的串联系统。以台湾一家非寿险公司为例，说明数据模糊时如何计算系统和流程效率以及如何推导它们之间的关系。

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