An integrated data envelopment analysis and free disposal hull framework for cost-efficiency measurement using rough sets

• We propose an integrated data envelopment analysis and free disposal hull framework.
• The proposed framework employs rough set theory to represent data uncertainty.
• First, a cost-efficiency analysis is developed for convex technologies with rough data.
• Then, rough cost-efficiency is extended to non-convex technologies.
• A case study in the Japanese banking industry shows the applicability of the proposed method.

Traditional cost-efficiency analysis methods require exact and precise values for inputs, outputs and input prices. However, this is not the case in many real-life applications. This study proposes a rough cost-efficiency approach to the problem of ranking efficient decision making units (DMUs). Based on rough set theory, a nonparametric methodology for cost-efficiency analysis is developed. The merits of this methodology include computational ease and the capacity to incorporate data uncertainty. Furthermore, it applies to both convex data envelopment analysis (DEA) and non-convex free disposal hull (FDH) technologies under different returns-to-scale assumptions. A numerical example and a real-life case study in the Japanese banking industry demonstrate the applicability of the proposed framework. In particular, the rankings of the DMUs resulting from the proposed models are compared with those obtained using the maximum technical efficiency loss index.

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