A new approach to rank the decision making units in presence of infeasibility in intuitionistic fuzzy environment

Data envelopment analysis (DEA) is a linear programming based methodology to determine the relative performance efficiencies of homogeneous decision making units (DMUs). In real world applications, some input and output datas do not possess crisp/fuzzy essence but they possess intuitionistic fuzzy (IF) essence. So, in this study, we develop an IF BCC (IFBCC) and an IF super efficiency BCC (IFSEBCC) model with triangular IF numbers (TIFNs) input/output data. Firstly, the efficiencies of DMUs are determined using IFBCC model. If DMUs are efficient then the super efficiencies of DMUs are determined using IFSEBCC model. If DMUs do not have feasible (finite) efficiencies/super efficiencies in intuitionistic fuzzy environment, then we can not rank the DMUs. Therefore, we develop IF models to determine the efficiencies of DMUs and ranking the DMUs in the presence of infeasibility in intuitionistic fuzzy environment. Two illustrative examples and one real life application are provided to illustrate the applications of the proposed IF models. Finally, comparison has been performed with the existing crisp models.