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Imprecise data envelopment analysis model with bifuzzy variables

Data envelopment analysis (DEA) is a non-parametric approach for measuring and evaluating the relative efficiencies of a set of entities with common crisp inputs and outputs. Whereas crisp input-output data are required in the traditional DEA evaluation process, the observed input-output data in real-world performance evaluation problems are quite often imprecise or vague. The impreciseness and vagueness related to the input-output data in DEA can be represented by fuzzy variables. The purpose of this paper is three-fold. First, the current study introduces a non-deterministic chance constrained DEA model, which solves the Charnes, Cooper and Rhodes (CCR) model by treating the input-output data as bifuzzy variables which are fuzzy variables with fuzzy parameters. Second, by assuming that decision making units operate in a bifuzzy environment, the study derives a deterministic model equivalent to the chance constrained model. Finally, two numerical examples are presented to demonstrate the applicability of the proposed framework.