Probabilistic linguistic term sets perform a particularly active role in the field of decision-making, particularly regarding decision-makers (DMs) who are inclined to convey evaluative information through natural linguistic variables. To effectively improve the current dilemma of multi-attribute group decision-making (MAGDM), this article put forward a new probabilistic linguistic MAGDM method with weighted Moment estimation. First, taking into account the psychological aspect of regret aversion among DMs, we use regret theory to transform the original decision-making matrix into the utility matrix, in which DMs usually exhibit limited rationality during the process of MAGDM. Then, a combined weighting method and a weighted Moment estimation model are investigated to determine the attribute weights, which are more scientifically and reasonably. Subsequently, in the process of consensus reaching process, a new trust propagation mechanism is designed to derive the weights of experts and the adjustment coefficients, in which we consider the shortest and longest propagation paths among DMs. Finally, an empirical validation of the MAGDM method's applicability is conducted utilizing raw coal quality assessment, accompanied by sensitivity and comparative analyses that underscore its advantages and robustness.

中文翻译：

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基于遗憾理论和加权 Moment 估计的有限理性共识达成过程


概率语言术语集在决策领域发挥着特别积极的作用，特别是对于倾向于通过自然语言变量传达评价信息的决策者 （DM）。为了有效改善当前多属性群决策 （MAGDM） 的困境，该文提出了一种新的加权矩估计的概率语言 MAGDM 方法。首先，考虑到 DMs 后悔厌恶的心理方面，我们利用后悔理论将原始决策矩阵转化为效用矩阵，其中 DMs 在 MAGMM 过程中通常表现出有限的理性;然后，采用组合加权法和加权 Moment 估计模型确定属性权重，更加科学合理。随后，在达成共识的过程中，设计了一种新的信任传播机制，推导了专家的权重和调整系数，其中我们考虑了 DM 之间最短和最长的传播路径。最后，利用原煤质量评估对 MAGDM 方法的适用性进行实证验证，并附有强调其优势和稳健性的敏感性和比较分析。