A Data Envelopment Analysis Model with Discretionary and Non-Discretionary Factors in Fuzzy Environments

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. The standard DEA models assume that all inputs and outputs are crisp and can be changed at the discretion of management. While crisp input and output data are fundamentally indispensable in the standard DEA evaluation process, input and output data in real-world problems are often imprecise or ambiguous. In addition, real-world problems may also include non-discretionary factors that are beyond the control of a DMU's management. Fuzzy logic and fuzzy sets are widely used to represent ambiguous, uncertain or imprecise data in DEA by formalizing the inaccuracies inherent in human decision-making. In this paper, we show that considering bounded factors in DEA models results in a disregard to the concept of relative efficiency since the efficiency of the DMUs are calculated by comparing the DMUs with their lower and/or upper bounds. In addition, we present a fuzzy DEA model with discretionary and non-discretionary factors in both the input and output-oriented CCR models. A numerical example is used to demonstrate the applicability and the efficacy of the proposed models