The Best–Worst Method (BWM) has been recently proposed to derive the weights of criteria using two vectors of the pairwise comparison. For BWM, the best criteria and the worst criteria of alternatives are first determined by the decision-maker (DM). Then, the DM gives his best-to-others vector (BV) and the others-to-worst vector (WV). In this paper, we show that the BV and WV can intrinsically be formulated as an incomplete reciprocal matrix, we call it BWM matrix. Thus, to derive the weights for BWM can be transformed to derive the weights from an incomplete reciprocal preference relation. In this view, we present several models to derive priority weights from a BWM matrix. Especially, we also show that the initial BWM model is a special case of our proposed method, the concept of efficiency is extended to the incomplete reciprocal preference relation. Furthermore, these methods are extended to derive the priority weights for group decision making problems. Additionally, some inconsistency indices are introduced to measure the inconsistency degree of a BWM matrix. Finally, one example is illustrated to derive the optimal weights from a BWM matrix and another example is illustrated to show the efficiency of the weight vectors, respectively. Monte Carlo simulations and comparative analyses are carried out to show the effectiveness of the proposed priority methods.

最近提出了最佳-最差方法（BWM）来使用成对比较的两个向量来推导标准的权重。对于 BWM，备选方案的最佳标准和最差标准首先由决策者 (DM) 确定。然后，DM 给出了他对其他人的最佳向量 (BV) 和其他人对最差向量 (WV)。在本文中，我们表明 BV 和 WV 本质上可以表示为不完全倒数矩阵，我们称之为 BWM 矩阵。因此，为了导出 BWM 的权重，可以转换为从不完全的互惠偏好关系中导出权重。从这个角度来看，我们提出了几个模型来从 BWM 矩阵中导出优先级权重。特别是，我们还表明初始 BWM 模型是我们提出的方法的特例，效率的概念被扩展到不完全的互惠偏好关系。此外，这些方法被扩展以导出群体决策问题的优先级权重。此外，还引入了一些不一致指标来衡量BWM矩阵的不一致程度。最后，说明了一个示例以从 BWM 矩阵导出最佳权重，并说明了另一个示例以分别显示权重向量的效率。进行了蒙特卡罗模拟和比较分析，以显示所提出的优先级方法的有效性。一个示例被说明以从 BWM 矩阵导出最佳权重，另一个示例被说明以分别显示权重向量的效率。进行了蒙特卡罗模拟和比较分析，以显示所提出的优先级方法的有效性。一个示例被说明以从 BWM 矩阵导出最佳权重，另一个示例被说明以分别显示权重向量的效率。进行了蒙特卡罗模拟和比较分析，以显示所提出的优先级方法的有效性。