Fuzzy Multi period efficiency and Malmquist productivity index in two stage

Two-stage fuzzy data envelopment analysis models measure the overall performance of a production system composed of two stages in a specified period of time, where variations in different periods are ignored .This paper takes the operations of individual periods into account to develop a multi-period two-stage fuzzy DEA model, which is able to measure the overall and period fuzzy efficiencies at the same time and then with the extension principle is utilized to develop a pair of two level mathematical programs in the various period for to calculate the lower and upper bounds of the α-cut of the fuzzy efficiency. The overall fuzzy efficiency of a decision making unit (DMU) in the specified period of time can be decomposed into the process fuzzy efficiency of each period. In this paper the fuzzy efficiencies measured from the model can also be used to calculate a common-weight and Malmquist productivity index (MPI) between two periods.