Efficiency of parallel production systems with fuzzy data

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 α 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.