Sensitivity analysis of the additive model in data envelopment analysis while inputs and outputs are fuzzy data

Abstract

Data envelopment analysis (DEA) requires input and output data to be precisely known. This is not always the case in real applications. Sensitivity analysis of the additive model in DEA is studied in this paper while inputs and outputs are symmetric triangular fuzzy numbers. Sufficient conditions for simultaneous change of all outputs and inputs of an efficient decision-making unit (DMU) which preserves efficiency are established. Two kinds of changes on inputs and outputs are considered. For the first state, changes are exerted on the core and margin of symmetric triangular fuzzy numbers so that the value of inputs increase and the value of outputs decrease. In the second state, a non-negative symmetric triangular fuzzy number is subtracted from outputs to decrease outputs and it is added to inputs to increase inputs. A numerical illustration is provided.

Keywords:

• DEA
• sensitivity analysis
• fuzzy data

2010 AMS Subject Classifications :

• 90B99
• 90C05

Notes

According to formula (28), j ε NB, in which NB is the set of non-basic variables, so in formula (39), j=1, 2, 6, 8 because the basic variables are so j=1 corresponds to corresponds to λ₂, j=6 corresponds to , and j=8 corresponds to .