Considering the influence of undesirable outputs in environmental assessments of the practical production process, this paper proposes a DEA cross-efficiency method and fuzzy preference relation based on semi-disposability of undesirable outputs for environmental assessments, which combines self-evaluation with peer-evaluation and avoids potentially unrealistic weighting scheme. We first develop a new input-oriented DEA model based on semi-disposability of undesirable outputs. Then, the corresponding DEA cross-efficiency method is proposed to evaluate the homogeneous decision-making units (DMUs) and the additive fuzzy preference relation is constructed using the DEA cross-efficiency scores. An output-oriented DEA model is adopted to derive the priority vector from the constructed additive fuzzy preference relation. Furthermore, we summarize the specific procedures for environmental assessments based on DEA cross-efficiency and fuzzy preference relation. Finally, the practical example of industrial environment assessment of the Yangtze River Economic Belt is provided to show the applicability and effectiveness of the proposed method.
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