Developing an Input Oriented Data Envelopment Analysis Model with Fuzzy Uncertainty in Variables

Abstract

Data Envelopment Analysis (DEA) technique is considered one of the most appropriate tool for assessing performance through calculating the technical efficiencies of a collection of related comparable organizations in transforming inputs into outputs. The conventional DEA methods require accurate measurement of both the inputs and outputs. However, the observed values of the input and output data in real-world problems are sometimes imprecise or vague, i.e. fuzzy. Imprecise evaluations may be the result of unquantifiable, incomplete and non-obtainable information. From the literature of fuzzy DEA applications, most if not all developed models considered all input and output variables as fuzzy, through adopting either the traditional DEA model or the output version of the model, and solved using the α-level approach. Accordingly, the main aim of this paper is to develop a Fuzzy Input Oriented DEA Model that considers a mix of both fuzzy and deterministic output and/or input variables to be solved using the α-cut approach. The developed model algorithm is divided into three stages; it starts by defining the membership function for the fuzzy variables (assumed triangular), then finding the α-cuts for the fuzzy variables, and finally calculating the relative efficiency for each decision making unit (DMU). The model is demonstrated through an illustrative example.