Incorporating hesitation in intuitionistic fuzzy slack based measure efficiency with an application to MGNREGA

The intuitionistic fuzzy set theory was introduced by Atanassov to lay focus on the hesitation present in a variable while deciding the degree of membership in fuzzy sets. The studies done on intuitionistic fuzzy sets deal extensively with the membership and non-membership function of the variables and pays little attention to the hesitation. The present study tries to dig deeper into the hesitation of triangular intuitionistic fuzzy numbers. We also try to establish the effect of hesitation on efficiency of decision making units. The hesitation and relative efficiency are inversely related. The presence of higher hesitation in a firm would lead to lower efficiency. In this study we have developed a mathematical model using SBM model to calculate the relative efficiency incorporated with hesitation in the decision making units and proposed a ranking algorithm to compare them. The proposed method has been applied to the scheme of MGNREGA to calculate the efficiencies of Indian States. The best performers have come out to be the States of Tamil Nadu, Andhra Pradesh and Tripura, whereas, the worst performers are the States of Manipur, Gujarat and Nagaland.