Effciency of Two-Stage Systems in Stochastic DEA

In the present world, there are many two-stage systems which provide information of inputs, outputs and intermediate measures which are imprecise, such as, (stochastic, fuzzy, interval etc). In these conditions, a two-stage data envelopment analysis or a (two-stage DEA method) cannot evaluate the effciencies of these systems. In several two-stage systems, the simultaneous presence of stages is necessary for the nal product. Hence, in this paper, we shall propose the stochas- tic multiplicative model and the deterministic equivalent, to measure the effciencies of these systems, primarily, in the presence of stochastic data, under the constant returns to scale (CRS) assumption, by using the non-compensatory property of the multiplication operator.Then, we will use the reparative property of the additive operation to propose the additive models as well as the deterministic equivalents, to calculate the effciencies of two-stage systems, in presence of stochastic data, under