OICC Press International Journal of Mathematical Modelling & Computations 2228-6233 2 1 2012 12 21 THE IDENTIFICATION OF EFFICIENCY BY USING FUZZY NUMBERS 53 59 EN M. Sanei Islamic Azad University, Central Tehran Branch, Iran. Iran, Islamic Republic of Department of Mathematics R. Dehghan Islamic Azad University, Masjed-Solyman Branch,Iran Iran, Islamic Republic of Department of Mathematics A. Mahmoodi Rad Islamic Azad University, Masjed-Solyman Branch,Iran Iran, Islamic Republic of Department of Mathematics Journal Article 2012 12 21 In original Data Envelopment Analysis (DEA) models for measuring the relative efficiencies of a set of Decision Making Units (DMUs) using various inputs to produce various outputs are limited to crisp data. To deal with imprecise data, the notion of fuzziness has been introduced. this paper develops a procedure to measure the efficiencies of DMUs with fuzzy observations. The basic idea is to transform a fuzzy DEA model to family of conventional crisp DEA models by applying optimistic, intermediate and pessimistic concepts. A numerical example is given to show the efficiency.