Evaluating the Efficiency of DMUs with Fuzzy Data via FDH Model

Data Envelopment Analysis (DEA) is a non-parametrical method for evaluating the efficiency of Decision Making Units (DMUs) using mathematical programming. The CCR model, the BCC model and the FDH model are well known as basic DEA models. These models based on the domination structure in primal form are characterized by how to determine the production possibility set from a viewpoint of dual form; the convex cone, the convex hull and the free disposable hull for the observed data, respectively. All these calculations occur when all data, that is the inputs and the outputs of Decision Making Units, are positive and crisp data. Now this question arises: if the data are Symmetric Triangular Fuzzy Number, how will be the method of computing the efficiency of Decision Making Units? In this article, we will introduce a method for evaluating the efficiency of Decision Making Units (DMUs) with FDH model when all data are symmetric triangular fuzzy numbers. The basic idea is to transform the fuzzy model into a crisp mixed integer linear programming problem by applying an α-cut approach. Finally, a numerical example is proposed to display the application of this method.

Data Envelopment Analysis, Free Disposable Hull, Mixed Integer linear programming, symmetrical triangular fuzzy number