基于 α-cut 区间的模糊最优-最劣方法用于多准则决策
An α-cut intervals based fuzzy best-Worst method for Multi-Criteria Decision-Making
AI总结：
针对模糊最优-最劣方法（FBWM）未充分利用模糊判断信息的问题，提出基于 α-cut 区间的 FBWM 模型，通过有限子集近似优化权重并引入 DoA、CI 和 CR 指标，有效减少信息损失并提升决策准确性。
摘要：
最优-最劣方法（Best-Worst Method, BWM）是一种著名的多准则决策（Multi-Criteria Decision-Making, MCDM）方法，用于在许多现实生活应用中计算准则权重。据观察，由于人的参与，用于在 BWM 中计算权重的决策判断可能是不精确的。为了将这种模糊性纳入权重计算中，Guo & Zhao 提出了一种使用模糊集的 BWM 模型，称为模糊 BWM（Fuzzy BWM, FBWM）。尽管已知该模型具有广泛的适用性，但它存在若干局限性。该现有模型最大的局限性之一在于，在权重计算中仅使用了模糊判断的下界、众数和上界值，而其他值未被使用。为了解决这一局限并优化整个形状，我们提出了一种基于 α-cut 区间的 FBWM 模型。这有助于减少信息损失。结果表明，尽管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] 的有限子集（设为 F）来近似最优权重。然后，我们开发了一种技术来测量权重集的近似度（Degree of Approximation, DoA），并获得具有所需 DoA 的权重集。对于给定的 F，近似权重是通过一个具有非线性性质的最小化问题来计算的，因此可能导致多个权重。为了解决这个问题，我们首先计算准则的所有近似权重的集合（这是一个区间），然后采用该区间的中心作为该准则的近似权重。为了测量权重集的准确性，我们为所提出的模型开发了一致性指数（Consistency Index, CI）和一致性比率（Consistency Ratio, CR）的概念。最后，我们讨论了一些数值示例以及所提出模型在供应链 4.0 风险因素排序中的实际应用，并将结果与现有模型进行了比较。
英文摘要：
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 α-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.
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