Parabolic Intuitionistic Fuzzy based Data Envelopment Analysis

Abstract

A Fuzzy Data Envelopment Analysis (FDEA) is a popular technique to measure the relative efficiency of a Decision Making Unit (DMU) with respect to other DMUs under uncertain/imprecise information represented in form of fuzzy input and fuzzy output. However, in a real life application, due to higher order of uncertainty, the fuzzy set may not be a suitable choice, as the membership value alone cannot represent the input/output information precisely. Therefore in the paper, we extend the FDEA model to Intuitionistic Fuzzy Data Envelopment Analysis (IFDEA) model, namely, Parabolic Intuitionistic Fuzzy based Data Envelopment Analysis, where the input and output are demonstrated by Parabolic Intuitionistic Fuzzy Numbers (PIFNs). Further the α-cut and s-cut approach are used to convert the parabolic intuitionistic fuzzy inputs and outputs into their corresponding intervals and to compute the parametric efficiencies of the given DMUs. Additionally, we have used the section formula to defuzzify the parabolic intuitionistic fuzzy numbers into their crisp form to execute the optimization problem. Finally, the cross-efficiency technique is used to rank the DMUs.