Parichehr zamani - Faculty of Engineering, Qom Branch, Islamic Azad University, Qom, Iran.

Traditional Data Envelopment Analysis (DEA) models evaluate the efficiency of decision making units (DMUs) with common crisp input and output data. However, the data in real applications are often imprecise or ambiguous. This paper transforms fuzzy fractional DEA model constructed using fuzzy arithmetic, into the conventional crisp model. This transformation is performed considering the goal programming that is one of the Multi Objective Programming (MOP) methods. Therefore, in this research the one linear programming model measures the fuzzy efficiencies of DMUs with fuzzy input and fuzzy output data.

Data envelopment analysis, Fuzzy input and fuzzy output data, Fuzzy efficiency, multiobjective programming, goal programming