Journal of Linear and Topological Algebra Vol. 04, No. 03, 2015, 165- 172 An algorithm for determining common weights by concept of membership function S. Saati a* , N. Nayebi a a Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran. Received 29 April 2015; Revised 17 November 2015; Accepted 15 December 2015. Abstract. Data envelopment analysis (DEA) is a method to evaluate the relative efficiency of decision making units (DMUs). In this method, the issue has always been to determine a set of weights for each DMU which often caused many problems. Since the DEA models also have the multi-objective linear programming (MOLP) problems nature, a rational relationship can be established between MOLP and DEA problems to overcome the problem of determining weights. In this study, a membership function was defined base on the results of CCR model and cross efficiency, and by using this membership function in a proposed model, we obtained a common set of weights for all DMUs. Finally, by solving a sample problem, the proposed algorithm was explained. c ⃝ 2015 IAUCTB. All rights reserved. Keywords: Data envelopment analysis (DEA), Cross efficiency, Membership function, Common set of weights, Multi-objective programming problem. 1. Introduction Charnes, Cooper, and Rhodes [2] presented CCR model to evaluate the efficiency of DMUs with several homogeneous inputs and outputs. In this model, a set of weights for each DMU is calculated and the CCR model determines the weights in such a way that the highest efficiency is obtained. One of the weaknesses of CCR models is that it makes zero the weights of the DMUs weight are not in our interest. It means when the input increases and the related output decreases, the model considered the related clause to be equal zero in order to obtain the maximum efficiency. Because of these problems and also due to the fact that the basic * Corresponding author. E-mail address: s saatim@iau-tnb.ac.ir (S. Saati). Print ISSN: 2252-0201 c ⃝ 2015 IAUCTB. All rights reserved. Online ISSN: 2345-5934 http://jlta.iauctb.ac.ir