Determine of the Malmquist Productivity Index Units in DEA on Fuzzy Inputs and Outputs

Data Envelopment Analysis (DEA) is an extremely flexible and useful methodology, which provides a relative efficiency score for each decision-making unit.Classic DEA models only evaluate the performance efficiency of units and they cannot provide any information about the progress and regress of units in two periods. Also, they suppose that all inputs and outputs are positive real numbers. But in the real world, due to the existence of uncertainty, this assumption may not always be true. So, the DEA models with fuzzy data (FDEA models) can more realistically represent real-world problems than the conventional DEA models. In this paper, we assume all inputs, outputs and efficiency measures are triangular fuzzy numbers. So we present a method for obtaining the fuzzy Malmquist productivity index on fuzzy data, and finally, we can determine progress and regression for units with fuzzy data.