Best Worst Method (BWM) is a multi-criteria decision-making method that is based on a structured pairwise comparison system. It uses two pairwise comparison vectors (best-to-others and others-to-worst) as input for an optimization model to get the optimal weights of the criteria (or alternatives). The original BWM involves a nonlinear model that sometimes results in multiple optimal weights meaning that the weight of each criterion is presented as an interval. The aim of this paper is to introduce a ratio, called concentration ratio, to check the concentration of the optimal intervals obtained from the nonlinear BWM. The relationship between the concentration ratio and the consistency ratio is investigated and it is found that the concentration ratio along with the consistency ratio of the model provides enhanced insights into the reliability and flexibility of the results of BWM.

中文翻译：

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非线性最佳最差方法的集中比

最佳最差方法 (BWM) 是一种基于结构化成对比较系统的多标准决策方法。它使用两个成对的比较向量（最佳到其他和其他到最差）作为优化模型的输入，以获得标准（或备选方案）的最佳权重。最初的 BWM 涉及一个非线性模型，该模型有时会产生多个最优权重，这意味着每个标准的权重都表示为一个区间。本文的目的是引入一个比率，称为集中率，以检查从非线性 BWM 获得的最佳区间的集中度。