Fuzzy free disposal hull models under possibility and credibility measures

Abstract

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.