Fuzzy free disposal hull models under possibility and credibility measures

The free disposal hull (FDH) models are used as an alternative to data envelopment analysis (DEA) models for performance measurement and efficiency assessment. The conventional FDH models are used to evaluate the performance of a set of firms or decision-making units (DMUs) using deterministic input and output data. However, the input and output data in the real-life performance evaluation problems are often imprecise and ambiguous. The impreciseness and ambiguity associated with the input and output data in FDH can be represented with fuzzy variables. In this paper, the concept of chance-constrained programming is used to develop FDH models with various returns to scale assumptions, including variable returns to scale (VRS), variable non-increasing returns to scale (NIRS), variable non-decreasing returns to scale (NDRS), and constant returns to scale (CRS), for efficient DMUs with fuzzy data. We propose two fuzzy FDH models with respect to possibility and expected value (credibility approach) constraints. Finally, a numerical example is presented to demonstrate the efficacy of the proposed procedures and algorithms.