TY - JOUR
T1 - Efficiencies of two-stage systems with fuzzy data
AU - Kao, Chiang
AU - Liu, Shiang Tai
N1 - Funding Information:
This research was supported by the National Science Council of the Republic of China under Contract: NSC98-2410-H-006-006-MY3.
PY - 2011/8/1
Y1 - 2011/8/1
N2 - 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 α, 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.
AB - 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 α, 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.
UR - https://www.scopus.com/pages/publications/79958107507
UR - https://www.scopus.com/pages/publications/79958107507#tab=citedBy
U2 - 10.1016/j.fss.2011.03.003
DO - 10.1016/j.fss.2011.03.003
M3 - Article
AN - SCOPUS:79958107507
SN - 0165-0114
VL - 176
SP - 20
EP - 35
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
IS - 1
ER -