الفهرس 
Developing a two-stage data envelopment analysis model for handling rough variables
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Abstract
The case in many real-life applications deals with complex, vague, imprecise, and
uncertain data. Traditional Data Envelopment Analysis (DEA) requires accurate and exact
inputs and outputs; hence it cannot deal with many practical problems. As well, traditional
DEA assumes the dependent relations among decision-making units (DMUs) are not
exist. In the traditional DEA DMUs are treated as black boxes where the initial inputs
enter the first stage and the final outputs from the second stage are only considered. The
intermediate stage is neglected to measure their efficiency. Therefore, the “black box”
theory reflects inaccurate efficiency indicators about systems consisting of complex
structures.
This research integrates classical DEA, a Two-stage network, and rough theory to
obtain a comprehensive evaluation. The proposed Two-stage RDEA model is a constant
return to scale (CRS) that measures the relative efficiencies of DMUs containing two
subprocesses while handling some uncertain rough variables in inputs and outputs.
The model is applied in the supply chain (Sc) to measure the efficiency of two
stages of the supply chain, including suppliers and manufacturers. The experimental
results showed the applicability of the proposed model to deal with the multistage system
containing uncertainty data. Moreover, we compare the traditional DEA with the twostage rough RDEA model and explain how to improve the relative efficiency. As well,
we enhanced our model to evaluate the multistage system, and apply it in a three-level
supply chain, including suppliers, manufacturers, and distributors. We also introduce
some recommendations for helping the decision-maker improve comprehensive
efficiency by changing trust-level (α).