Data Envelopment Analysis with Fuzzy Parameters : An Interactive Approach

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. In the conventional DEA, all the data assume the form of specific numerical values. However, the observed values of the input and output data in real-life problems are sometimes imprecise or vague. Some researchers have proposed various fuzzy methods for dealing with the imprecise and ambiguous data in DEA. However, these methods do not consider the preferences of the decision makers (DMs) in the evaluation process. We propose an interactive evaluation process for measuring the relative efficiencies of a set of DMUs in fuzzy DEA with consideration of the DMs’ preferences. We construct a linear programming (LP) model with fuzzy parameters and calculate the fuzzy efficiency of the DMUs for different α levels. Then, the DM identifies his/her most preferred fuzzy goal for each DMU under consideration. A modified Yager index is introduced and used to develop a ranking order of the DMUs. The main thrust of this study is to allow the DMs to use their preferences or value judgments when evaluating the performance of the DMUs. A numerical example is presented to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures and algorithms