Performance Efficiency of Public Health Sector Using Intuitionistic Fuzzy DEA

Abstract

Out of several generalizations of fuzzy set theory for various objectives, the notions of intuitionistic fuzzy sets (IFSs) is very useful in modeling real life problems. In existing fuzzy data envelopment analysis (FDEA) models, the inputs and outputs are limited to fuzzy input and fuzzy output data. In real life problems, the input data and output data can be considered as linguistic/vague characterized by intuitionistic fuzzy numbers (IFNs). So, in the present study, we extend FDEA to intuitionistic FDEA (IFDEA) in which the input and output data are taken as IFNs, in particular triangular IFNs (TIFNs). In this study, we develop models to measure the efficiencies of each DMU in intuitionistic fuzzy environment using α and β-cuts and we get IF interval efficiencies. The ranking of FNs has been studied by many authors and extended to IFNs because of its applicability in real life problems. The ranking of IF interval efficiency plays an important role in DEA where the interval analysis is essential. Further, in this paper a new method for ranking IF interval efficiencies has been proposed and compared with other existing methods. A new general minimax approach is proposed to compare and rank the IF efficiency intervals of DMUs. One numerical example is provided to show the applications of the proposed IFDEA model and the proposed ranking approach. Moreover, we present an application of the proposed approach to the public health sector.