Cubic Fermatean fuzzy sets offer a flexible and powerful tool for decision-making, permitting decision-makers to incorporate uncertainty and reluctance into their decision-making process, and enabling them to make more informed and effective decisions in complex and uncertain situations. We present cubic fermatean fuzzy set and operational laws. We offer some cubic fermatean fuzzy numbers, as well as some cubic fermatean fuzzy aggregation operators, such as the cubic fermatean Einstein fuzzy weighted geometric operator, the cubic fermatean Einstein fuzzy ordered weighted geometric operator, and the cubic fermatean Einstein fuzzy hybrid weighted geometric operator. To demonstrate the solution to complicated real-life problems, an algorithm for the MADM problem is established under a system of cubic fermatean fuzzy information. To check the possibility of proposed aggregation approaches, we provided a numerical example to choose the desirable best options by using conceived approaches. To disclose the suppleness and applicability of designed methods, sensitive study, and comparative study are illustrated by complementary findings of existing methods with presently developed approaches.

中文翻译：

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基于三次费马爱因斯坦模糊加权几何算子的群决策

三次费马模糊集为决策提供了灵活而强大的工具，允许决策者将不确定性和不情愿纳入决策过程，使他们能够在复杂和不确定的情况下做出更明智、更有效的决策。我们提出三次费马模糊集和运算法则。我们提供了一些三次费马模糊数，以及一些三次费马爱因斯坦模糊聚合算子，例如三次费马爱因斯坦模糊加权几何算子、三次费马爱因斯坦模糊有序加权几何算子和三次费马爱因斯坦模糊混合加权几何算子。为了演示复杂现实问题的解决方案，在三次费马模糊信息系统下建立了MADM问题的算法。为了检查所提出的聚合方法的可能性，我们提供了一个数值示例，通过使用设想的方法来选择理想的最佳选项。为了揭示所设计方法的灵活性和适用性，敏感研究和比较研究通过现有方法与目前开发的方法的互补发现来说明。