Data Envelopment Analysis and Decision Science 2014 (2014) 1-10 Available online at www.ispacs.com/dea Volume 2014, Year 2014 Article ID dea-00058, 10 Pages doi:10.5899/2014/dea-00058 Research Article Ranking units with fuzzy data in DEA Mohammad Khodabakhshi 1 ∗ , Kourosh Aryavash 2 (1) Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran. (2) Department of Mathematics, Faculty of Science, Lorestan University, Khorram Abad, Iran. Copyright 2014 c ⃝ Mohammad Khodabakhshi and Kourosh Aryavash. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this study, both optimistic and pessimistic approaches of data envelopment analysis are applied to propose an equi- table ranking method in fuzzy environments. To this end, we suppose that the sum of efficiency scores of all decision making units (DMUs) equals to unity. Using the worst-best and best-worst approaches, the minimum and maximum possible efficiency scores of each DMU are estimated at some α -levels. Then, a number of such scores are used to construct the corresponding fuzzy score. Finally, using a defuzzification method the obtained fuzzy score is trans- formed into crisp score. DMUs are ranked according to their crisp scores. Keywords: Data envelopment analysis; Ranking; Fuzzy. 1 Introduction Data envelopment analysis (DEA) is a linear programming (LP) technique which measures the relative efficiency of peer decision making units (DMUs) when multiple inputs and outputs are present. The first model of DEA (CCR) was introduced by Charnes et al. (CCR) [5] in 1978. To see the other classic models of DEA, the readers can see [3, 6, 9, 31]. The pioneering DEA models divide DMUs into two efficient and inefficient groups while in practice, there is often a need to fully rank them. So far, several ranking methods are presented in the DEA literature [1]. Andersen and Peterson [2] proposed the super efficiency models for ranking only efficient units in the DEA. This method removes the under assessment unit from the set of DMUs and evaluates the distance of DMU from the new efficient frontier. Cook et al. [7] developed prioritization models to rank only the efficient units. Cross-efficiency approach is another ranking method that was proposed by Sexton et al. [30]. This approach evaluates the performance of a DMU with respect to the optimal input and output weights of other DMUs. Wang and Chin [33] proposed another cross-efficiency model known as Neutral DEA model to gain one set of input and output weights for each DMU. The benchmarking ranking of DEA efficient DMUs initially developed by Torgersen et al. [32]. In this method, efficient DMUs are ranked based on their importance as a benchmark for the other DMUs. Cooper and Tone [8] ranked the DMUs according to scalar measures of inefficiency in DEA, based on the slack variables. Liu and Peng [26] proposed Common Weights Analysis (CWA) to determine a set of indices for common weights to rank efficient DMUs of DEA. Employing the set of common weights, the absolute efficiency score of each DMU in the efficient category is recomputed. Khodabakshi [15] presented a super-efficiency model based on improved outputs in DEA. Also, Khodabakshi et al. [19, 21] and Khodabakshi [20] proposed some super efficiency models in the stochastic environment. Khodabakhshi [18] and Khodabakhshi et al. [20] extend some DEA models from the deterministic environment to the stochastic one. Also, ∗ Corresponding author. Email address: mkhbakhshi@yahoo.com