Cubic q-rung orthogonal fuzzy sets (C q-ROFSs) are a sophisticated mathematical tool used to handle complex evaluation information in multi-attribute decision-making problems. In specific decision-making problems, the power Bonferroni mean (PBM) operator can reflect the correlation between different attributes and mitigate the impact of extreme evaluation information, thereby providing more practical value. This paper focuses on expanding the PBM operator into the C q-ROFS environment and deriving new PBM operators: the cubic q-rung orthogonal power Bonferroni averaging operator and weight cubic q-rung orthogonal PBM operator. The proposed operator shows strong flexibility and stability in the cubic q-rung orthogonal fuzzy environment. In the absence of weight information, there is a dearth of literature addressing the acceptable advantage and decision stability in the C q-ROFS environment; considering the regret behavior of decision information, a VIKOR method based on regret theory is proposed. The proposed method aggregates information using the proposed operator, determines the scheme and weights at two levels of attributes, and constructs a relative proximity decision matrix. Then, the VIKOR method calculates the group utility value and individual regret value based on the regret perception value to rank the alternatives. Finally, the method is applied to evaluate the cotton foreign fiber content, and its stability and effectiveness are verified through sensitivity analysis and comparison with existing methods.

中文翻译：

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基于异纤含量等级评定方法的幂Bonferroni均值算子的开发与应用

三次 q 梯级正交模糊集 (C q-ROFS) 是一种复杂的数学工具，用于处理多属性决策问题中的复杂评估信息。在具体决策问题中，幂邦费罗尼均值（PBM）算子可以反映不同属性之间的相关性，减轻极端评价信息的影响，从而提供更多的实用价值。本文重点是将 PBM 算子扩展到 C q-ROFS 环境中并推导新的 PBM 算子：三次 q 梯级正交幂 Bonferroni 平均算子和权重三次 q 梯级正交 PBM 算子。所提出的算子在三次q-梯级正交模糊环境中表现出很强的灵活性和稳定性。在缺乏权重信息的情况下，缺乏讨论 C q-ROFS 环境中可接受的优势和决策稳定性的文献；考虑决策信息的后悔行为，提出一种基于后悔理论的VIKOR方法。该方法使用所提出的算子聚合信息，确定两个属性级别的方案和权重，并构造相对邻近度决策矩阵。然后，VIKOR方法根据后悔感知值计算群体效用值和个人后悔值，对备选方案进行排序。最后将该方法应用于棉花异纤含量评价，并通过敏感性分析以及与现有方法的比较，验证了其稳定性和有效性。