A Parabolic Based Fuzzy Data Envelopment Analysis Model with an Application

A Fuzzy Data Envelopment Analysis (FDEA) is a popular technique to measure the relative efficiency of decisionmaking units (DMUs) with imprecise and vague data for multiple inputs and outputs. In real-life applications, there are two types of outputs: desirable outputs and undesirable outputs. In this paper, we have proposed a new version of FDEA model, named as Parabolic based Fuzzy Data Envelopment Analysis (PFDEA) model that computes parametric efficiency of a DMU in the presence of undesirable outputs. The inputs and outputs are represented in the form of asymmetric parabolic fuzzy numbers in the proposed model. A new technique is introduced to convert PFDEA model into a linear programming problem using α-cut approach with a novel section formula based method, named as Ratio Division Method. This method is used to perform the complete ranking of the DMUs in a numerical example using Cross-Efficiency Method to provide a complete ranking of the DMUs.