Evaluating the Multi-period Systems Efficiency in the Presence of Fuzzy Data

In many real world applications, the efficiency of production systems should be determined in multiple periods of time while inputs and outputs are imprecise and fuzzy. However, the relative efficiencies of decision making units (DMUs) in the traditional data envelopment analysis (DEA) models are usually measured in a particular period of time and in the presence of precise inputs and outputs. Therefore, the current paper proposes a method to measuring the overall and period efficiencies of DMUs under uncertainty. Actually, a fuzzy DEA approach, which has been based on a fuzzy expected value method, is suggested to calculate the performance of DMUs with fuzzy input/output factors in several periods of time. Furthermore, efficiency changes of DMUs are handled in fuzzy multi-period systems by global Malmquist productivity index (MPI) with common-weights. The proposed approach is illustrated and clarified with two numerical examples. The introduced method can be utilized in the presence symmetrical and asymmetrical fuzzy numbers.