Fatemeh Komaki - Department of Mathematics, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran
Reza Fallahnejad - Department of Mathematics, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran
Farhad Losseinzadeh Lotfi - Department of mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Mohsen Rostamy_Malkhalifeh - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

AbstractAs the calculated efficiencies for the DMUs is relative, so each DMU attempts to improve its performance to don’t miss the position of efficiency in compete with other DMUs. Generally, the performance of DMUs can be evaluated from two perspectives-optimistic and pessimistic. A part of data envelopment analysis examines the sensitivity of the set of efficient DMUs to changes in input and output values. In real world, DEA is sometimes faced with fuzzy and interval inputs and/or outputs. In this paper we focus on the one of important subjects of sensitivity analysis and present an algorithm which uses the classic fuzzy DEA models that can determine the relative efficiency security margin of DMUs with fuzzy and interval inputs and outputs and their simultaneous perturbation. Of course, in addition to the optimistic frontier, we also consider the pessimistic frontier for the observed DMUs and call it the inefficiency improvement margin. With this information, the managers of companies can identify their closest threat and improve their performance in order to keep their position in ranking. Some numerical examples for illustration are given.

Data envelopment analysis, Sensitivity analysis, fuzzy efficiency security margin