The Identi fication of E fficiency by Using Fuzzy Numbers

Traditional Data Envelopment Analysis (DEA) models for measuring the relative e fficiencies of a set of Decision Making Units (DMUs) the using various inputs to produce various outputs are limited to crisp data. In real world situations, however, this assumption may not always be true. When some inputs and outputs are unknown decision variables,such as fuzzy data, rough data, interval data, the DEA model is called imprecise DEA. 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 effi ciency.