Data Envelopment Analysis (DEA) is a prominent technique for evaluating the performance and ranking of a set of decision-making units (DMUs) that transform multiple inputs into multiple outputs. However, one of the challenges of the primary DEA models is facing imprecise data in real practical problems. To address this issue, fuzzy DEA have been proposed, which have been successfully applied in many real fields. On the other hand, in some real-world DEA applications, the primary objective of performance evaluation is the ranking of a group that consists of several DMUs that are typically under the control of a centralized management. In this paper, we try to use the theory of cooperative games and Shapley value method as a fair method to solve such games in order to rank groups in DEA. In this way, the resulting rank for groups is based on the average marginal shares of groups in different coalitions that are formed based on the theory of cooperative games. We applied the proposed method to rank groups of airlines considering fuzzy data. To the best of authors' knowledge, so far, no method has been presented in DEA literature for ranking groups in fuzzy environment and using game theory techniques.