two-stage dea with fuzzy data

data envelopment analysis is a nonparametric technique checking efficiency of dmus using math programming. in conventional dea, it has been assumed that the status of each measure is clearly known as either input or output. kao and hwang (2008) developed a data envelopment analysis (dea) approach for measuring efficiency of decision processes which can be divided into two stages. the first stage uses inputs to generate outputs which become the inputs to the second stage. the first stage outputs are referred to as intermediate measures. the second stage then uses these intermediate measures to produce outputs. the data are crisp in the standard dea model whereas there are many problems in the real life in which data may be uncertain. thus, in this paper, a fuzzy version of two-stage dea model with a symmetrical triangular fuzzy number is presented. the basic idea is to transform the fuzzy model into crisp linear programming by using  approach. finally, a numerical example is proposed to display the application of this method.