标题： 基于α截集的模糊最佳-最差多准则决策方法 显示英文标题

标题： An α-cut intervals based fuzzy best-Worst method for Multi-Criteria Decision-Making

摘要： 最佳-最差法（BWM）是一种著名的多准则决策方法（MCDM），用于计算许多实际应用中的准则权重。观察到在BWM中用于计算权重的决策判断可能由于人为因素而不准确。为了将这种模糊性纳入权重计算，Guo & Zhao提出了一个使用模糊集的BWM模型，称为模糊BWM（FBWM）。尽管该模型被认为具有广泛的应用性，但它有几个局限性。这个现有模型最大的局限性之一是，在权重计算中使用了模糊判断的下限、模值和上限，而其他值未被使用。为了解决这一限制并优化整个形状，我们提出了一种基于{\alpha }-切割区间的FBWM模型。这有助于减少信息损失。结果表明，虽然可以同时优化整个形状，但这样做很困难。因此，我们使用[0, 1]的一个有限子集F来近似最优权重。然后，我们开发了一种测量权重集的近似度（DoA）的技术，并获得具有所需DoA的权重集。对于给定的F，使用一个具有非线性性质的最小化问题来计算近似权重，这可能导致多个权重。为了解决这个问题，我们首先计算所有准则近似权重的集合，这是一个区间，然后采用该区间的中心作为准则的近似权重。为了衡量权重集的准确性，我们为所提出的模型开发了相容性指数（CI）和相容性比率（CR）的概念。最后，我们讨论了一些数值例子和所提出模型在供应链4.0风险因素排名中的实际应用，并将结果与现有模型进行了比较。 显示英文摘要

摘要： The Best-Worst Method (BWM) is a well-known Multi-Criteria Decision-Making (MCDM) method used to calculate criteria-weights in many real-life applications. It was observed that the decision judgments used to calculate weights in BWM may be imprecise due to human involvement. To incorporate this ambiguity into the weight calculation, Guo & Zhao proposed a model of BWM using fuzzy sets, known as Fuzzy BWM (FBWM). Although this model is known to have wide applicability, it has several limitations. One of the biggest limitations of this existing model is that the lower, modal and upper values of the fuzzy judgment are used in the weight calculation and the other values remain unused. To solve this limitation and optimize the entire shape, we propose a model of FBWM based on {\alpha}-cut intervals. This helps in reducing information loss. It turns out that although it is possible to optimize the entire shape simultaneously, it is difficult to do so. Therefore, we approximate optimal weights using finite subset, say F, of [0, 1]. We then develop a technique to measure the Degree of Approximation (DoA) of a weight set and obtain a weight set with the desired DoA. For a given F, approximate weights are calculated using a minimization problem that has a non-linear nature and thus may lead to multiple weights. To solve this issue, we first compute the collection of all approximate weights of the criterion, which is an interval, and then adopt the center of this interval as the approximate weight of the criterion. To measure the accuracy of a weight set, we develop the concepts of Consistency Index (CI) and Consistency Ratio (CR) for the proposed model. Finally, we discuss some numerical examples and a real-world application of the proposed model in ranking of risk factors in supply chain 4.0 and compare the results with existing models.