Journal
FUZZY SETS AND SYSTEMS
Volume 176, Issue 1, Pages 20-35Publisher
ELSEVIER
DOI: 10.1016/j.fss.2011.03.003
Keywords
Data envelopment analysis; Efficiency; Series system; Fuzzy data; Two-level mathematical program
Funding
- National Science Council of the Republic of China [NSC98-2410-H-006-006-MY3]
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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 alpha-cut of the fuzzy efficiency. By enumerating various values of alpha, 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. (C) 2011 Elsevier B.V. All rights reserved.
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