Rough set theory expresses vagueness, not by means of membership, but employing a boundary region of a set. If the boundary region of a set is empty, it means that the set is crisp. Otherwise, the set is rough. Nonempty boundary region of a set means that our knowledge about the set is not sufficient to define the set precisely. In this paper, a rough programming (RP) problem is introduced where a rough function concept and its convexity and differentiability depending on the boundary region is studied. The RP problem is converted into two subproblems namely, lower and upper approximation problem. The Kuhn-Tucker. Saddle point of rough programming problem (RPP) is discussed. In addition, in the case of differentiability assumption the solution of the RP problem is investigated A numerical example is given to illustrate the methodology. Manuscript profile

The existence of a performance evaluation system is inevitable due to the dramatic changes in the business environment. The comprehensive performance evaluation attempts to identify institutional units' potential strength and role in influencing the organizations' performance. This study aims to analyze the performance evaluation according to seven dimensions of the Sink and Tuttle model using data envelopment analysis. The result of the seven dimensions of the Sync-Tuttle model is the creation of a comprehensive performance evaluation system in organizations, which leads to the improvement of organizational performance. The proposed model covers all essential performance indicators and takes steps with more generalizability and more realistic evaluation than other performance evaluation systems.In this research, the performance of eight organizational units of the NIPA Company has been evaluated. A total of seven variables of the Sink-Tuttle model are input, and the performance level of organizational units is the output of the proposed model. Coordination between strategies, organizational learning, and knowledge management is recommended to improve organizational performance. The overlap of the evaluation results in the sink and Tuttle model and the data envelopment analysis indicates the validity of the proposed model.Action in the inefficient units can be taken by implementing training, changing key people, developing a participatory system, establishing a performance evaluation system with appropriate criteria, and developing management based on purpose. The results of the proposed performance evaluation model can be used as the main part of formulating and implementing organizations' policies. Manuscript profile