Ranking DMUs with interval data using DEA and CA approaches R. Behmanesh 1 , K. Kianfar 2 , E. Najafi 3 1,2,3 Azad University, Science and Research branch, Iran ( 1 rezaehs@yahoo.com, 2 kianoosh.kianfar@yahoo.com, 3 Najafi1515@yahoo.com) Abstract-Data envelope analysis (DEA) is an approach to estimate the relative efficiency of decision making units (DMUs). Several studies were conducted in order to prioritize efficient units and some useful models such as cross-efficiency matrix (CEM) were presented. Besides, a number of DEA models with interval data have been developed and ranking DMUs with such data was solved. However, presenting an obtained crisp data derived interval data is a critical problem, so that many researches were implemented so as to compute weights and averaging the interval data. In this paper we propose the new algorithm to find more suitable weight applying a data mining approach of DMU’s data. For this purpose, we employed clustering and pair-wise comparison matrix on given relative efficiency from CEM. Results indicate there is meaningful different between efficiency of DMUs with lower bound and that of DMUs with upper bound. Keywords- Data evelope analysis, Cross-efficiency matrix, Cluster analysis I. INTRODUCTION Data envelop analysis (DEA) is a linear programming model and non-parametric approach that evaluates relative technical efficiencies of decision making units (DMUs) on the basis of multiple inputs and outputs by computing the ratio of weighted sum of their outputs to their inputs (Arieh and Gullipalli, 2012; Jahanshahloo et al, 2009; Smirlis et al, 2006). This technique has been used in many fields successfully with crisp values, however in real application there are inaccurate data similar to probabilistic, interval, ordinal, qualitative, or fuzzy. Hence, some researchers conducted several theoretical development of DEA model with data such as interval (Despotis and Smirlis, 2002; Jahanshahloo et al, 2004; Jahanshahloo et al, 2009). Nevertheless, there are many models and techniques to solve this problem, but there is a new problem for ranking the efficient DMUs with interval data, so that in some researches DMUs were ranked by these ideal points (Jahanshahloo et al, 2011; Wu et al, 2013). There are several models to rank DMUs with crisp data (Hashimoto and Wu, 2004). However, in all researches, ranking DMUs with interval data has been solved by using ranking approaches such as AHP or TOPSIS or hybrid algorithm to find suitable weight in order to calculate crisp efficiency basis of interval inputs and outputs. Therefore, we conduct new approach using data mining techniques similar to clustering to obtain these weights as new model. II. OVERVIEW OF THE RESEARCH TECHNIQUES A. DEA models In the previous section DEA technique was defined completely. In this part we describe existing models related to DEA. There are three commonly orientations for DEA model, which can be formulated as below: 1. Input oriented model is related to the minimizing level of the inputs in order to achieve a given level of the outputs. ∑ ∑ = = = s r rp r m i ip i p y u x v 1 1 min θ Subject to n j y u x v s r rj r m i ij i ,..., 1 1 1 1 = ≤ ∑ ∑ = = (1) 0 , ≥ i r v u 2. Output oriented model is concerned with the maximizing level of the outputs per given level of the inputs (Zohrehbandian & Sadeghi, 2013; Samoilenko et al, 2008; Caklovic & Hunjak, 2012). ∑ ∑ = = = m i ip i s r rp r p x v y u 1 1 max θ Subject to n j x v y u m i ij i s r rj r ,..., 1 1 1 1 = ≤ ∑ ∑ = = (2) 0 , ≥ i r v u 3. Base oriented model unlike the others, is pertains to the optimal combination of the inputs and outputs. Consequently, this model has control over inputs as well as outputs, concluding the efficiency of input utilization and efficiency of output production (Samoilenko et al, 2008). Instead of exact data, we will apply models with interval data in order to rank DMUs. Input oriented with interval data for upper bound efficiency and lower efficiency is formulated, respectively as below: Upper bound efficiency: Advances in Business and Economic Development ISBN: 978-1-61804-273-6 288