Development of intuitionistic fuzzy data envelopment analysis model based on interval data with an application to MGNREGA 2018-19

In modelling real life problems, intuitionistic fuzzy variables are best way of modelling linguistic variables. They can express the vagueness of variables to a greater extent. In this paper, we develop a new approach for measuring relative efficiency of decision making units (DMUs) with intuitionistic fuzzy inputs and outputs. Derived from data envelopment analysis (DEA) and interval DEA, the proposed model calculates the relative efficiency of a DMU in the form of an interval. The merit of the proposed model over the existing methods is justified comparison of units over the same production possibility set (PPS). We also develop a ranking algorithm for comparison of DMUs. Another merit of the proposed method is almost uniform ranking of DMUs for different α and β. We verify the proposed model using an example and apply our model to the scheme of MGNREGA. We check the efficiency intervals and calculate the ranking of Indian States and Union Territories. The states of Telangana, West Bengal and Jharkhand have emerged as the best performing states. The worst performers are the states of Karnataka, Nagaland, Bihar and Goa.