Development of intuitionistic fuzzy super-efficiency slack based measure with an application to health sector

Data envelopment analysis (DEA) is a linear programming based technique, which determines the performance efficiencies of homogeneous decision making units (DMUs). Slack based measure (SBM) model finds the performance efficiency, and it deals with the input excesses and output shortfalls of DMUs. In conventional SBM, the data is crisp. But it fluctuates in the real world applications. Such data can take the form of fuzzy/intuitionistic fuzzy (IF) number. In this paper, we propose an IF slack based measure (IFSBM) model to determine the efficiency of DMUs and IF super efficiency SBM (IFSESBM) model to determine the efficiency of efficient DMUs for a in (0,1] and beta in [0,1). Also, we propose a ranking method for intuitionistic fuzzy interval numbers (IFINs) based on alpha and beta-cuts. Finally, a health sector application of the proposed model is presented with two IF inputs: (i) number of beds (ii) number of doctors and two IF outputs: (i) number of pathology operations (ii) number of minor surgeries.