Fuzzy Stochastic Data Envelopment Analysis with Undesirable Outputs and its Application to Banking Industry

Data envelopment analysis (DEA) is a widely used technique for measuring the relative efficiencies of decision-making units (DMUs) with multiple inputs and multiple outputs. The classical DEA models were initially formulated only for desirable inputs and outputs. However, undesirable outputs may be present in the production process which needs to be minimized. In addition, in real-world problems, the observed values of the input and output data are often vague or random. Indeed, decision makers may encounter a hybrid uncertain environment where fuzziness and randomness coexist in a problem. In order to deal with the above problems, this paper proposes fuzzy stochastic DEA model with undesirable outputs. Three fuzzy DEA models with respect to probability–possibility, probability–necessity and probability–credibility constraints are applied. The contribution of this paper is fourfold: (1) the proposed approach considers the impact of undesirable outputs on the performance of DMUs; (2) unlike the existing methods, the proposed solution approach provides efficiency scores in the range of zero and one for all DMUs; (3) the proposed approach analyzes the influence of the presence of both fuzzily imprecision and probabilistic uncertainty in the data over the efficiency results; and (4) a case study in the banking industry is presented to exhibit the efficacy of the procedures and demonstrate the applicability of the proposed model.