TY - JOUR

T1 - Efficiency of parallel production systems with fuzzy data

AU - Kao, Chiang

AU - Lin, Pei Huang

N1 - Funding Information:
This research was supported by the National Science Council, Republic of China (Taiwan), under Grant NSC98-2410-H-006-006-MY3.

PY - 2012/7/1

Y1 - 2012/7/1

N2 - 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.

AB - 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.

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U2 - 10.1016/j.fss.2012.01.004

DO - 10.1016/j.fss.2012.01.004

M3 - Article

AN - SCOPUS:84859588396

SN - 0165-0114

VL - 198

SP - 83

EP - 98

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

ER -