The analytic hierarchy process (AHP) is widely used as a multi-criteria decision-making method in practical applications. Several researchers have expanded the AHP method to D numbers AHP (D-AHP) to apply AHP to an uncertain decision-making environment. D numbers is an extension of the Dempster–Shafer (D–S) theory, which overcomes the shortcomings of the D–S theory and can effectively express uncertain information. With the deepening of research on the AHP method, the best–worst method (BWM) was proposed as an improvement to the AHP method. The BWM can lower the inconsistency in results and reduce the number of required pairwise comparisons. Although some researchers have extended the BWM method to an uncertain environment and proposed fuzzy BWM methods, these methods cannot handle some special situations, such as when the subjective evaluations of experts are conflicting or altogether missing. To apply the BWM method to these special situations, this study suggests combining the BWM with D numbers and proposes D numbers BWM (D-BWM) weighting model. First of all, we discuss D numbers extended fuzzy preference relations (DNFPRs). Afterwards, we design an algorithm to select the best and worst criteria based on the DNFPRs by calculating the out-degrees and in-degrees. Furthermore, we develop a linear programming model to derive the weights of criteria, and then propose a consistency ratio to check the reliability of the derived results. The experimental results show that the D-BWM method is more suitable for realistic decision-making because of its simplicity and sensitivity to subjective information. Finally, the proposed method is applied to evaluate the environmental performances of 30 provincial administrative regions of China.

层次分析法（AHP）在实际应用中被广泛用作多准则决策方法。一些研究人员已将AHP方法扩展到D数AHP（D-AHP），以将AHP应用于不确定的决策环境。D数字是Dempster-Shafer（DS）理论的扩展，它克服了DS理论的缺点，可以有效地表达不确定的信息。随着对AHP方法的研究的不断深入，提出了最差方法（BWM）作为对AHP方法的改进。BWM可以减少结果的不一致，并减少所需的成对比较的次数。尽管一些研究人员已将BWM方法扩展到不确定的环境并提出了模糊BWM方法，但这些方法无法处理某些特殊情况，例如专家的主观评价相互矛盾或完全缺失时。为了将BWM方法应用于这些特殊情况，本研究建议将BWM与D数相结合，并提出D数BWM（D-BWM）加权模型。首先，我们讨论D数扩展模糊偏好关系（DNFPR）。之后，我们设计了一种算法，通过计算出学位和入学位，根据DNFPR选择最佳和最差的标准。此外，我们建立了一个线性规划模型来推导准则的权重，然后提出一个一致性比率来检验推导结果的可靠性。实验结果表明，D-BWM方法具有简单性和对主观信息的敏感性，因此更适合于现实决策。最后，