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Efficiency of parallel production systems with fuzzy data

机译：具有模糊数据的并行生产系统的效率

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This paper investigates the problem of efficiency measurement for parallel production systems where a number of processes are operating independently within the system, and some input/output data are fuzzy numbers. When all observations have precise values, previous studies found that the system efficiency measured from a relational data envelopment analysis model is a weighted average of the process efficiencies. Based on the extension principle of fuzzy theory, this paper constructs a pair of two-level programming models to calculate the lower and upper bounds of the α-cuts of the fuzzy system and process efficiencies. It is shown that the fuzzy system efficiency is still a weighted average of the fuzzy process efficiencies. However, the weights need not be the same at different a levels. The case of measuring the teaching and research efficiencies of chemistry departments in UK universities with a qualitative factor of research quality discussed in the literature is used as an example to explain the idea of this paper. Fuzzy measures obtained from fuzzy observations are more informative than crisp measures obtained from assuming the fuzzy observations to be precise.
机译：本文研究了并行生产系统的效率测量问题，在并行生产系统中，多个过程在系统中独立运行，并且某些输入/输出数据是模糊数。当所有观察值都具有精确值时，以前的研究发现，从关系数据包络分析模型测得的系统效率是过程效率的加权平均值。基于模糊理论的扩展原理，构建了两个两级规划模型来计算模糊系统的α-割线的上下限和过程效率。结果表明，模糊系统效率仍然是模糊过程效率的加权平均值。但是，权重不必在不同的级别上相同。本文以文献中讨论的具有定性研究质量为衡量标准的英国大学化学系教学与研究效率测​​算案例为例进行说明。从模糊观测获得的模糊测度比从假设模糊观测得到的精确测度得到的信息更丰富。

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