Algebraic operations are used effectively in decision-making problems. Especially, Dombi, Hamacher and Einstein algebraic operators are used frequently in the decision-making field. On the other hand, it is known that aggregation operators affect the decision-making process in decision-making problems. In this paper, we used Dombi operations to develop some Fermatean fuzzy aggregation operators. Arithmetic and geometric analysis of each aggregation method were performed. We defined the following operators: Fermatean fuzzy Dombi weighted average operator, Fermatean fuzzy Dombi weighted geometric operator, Fermatean fuzzy Dombi ordered weighted average operator, Fermatean fuzzy Dombi ordered weighted geometric operator, Fermatean fuzzy Dombi hybrid weighted average operator, Fermatean fuzzy Dombi hybrid weighted geometric operator. Also, an analysis was performed for the beta value of the Dombi parameter. Properties of proposed operators were presented, and operators were defined on Fermatean fuzzy sets. Finally, proposed operators were compared with the existing aggregation operators. To understand the impact of the proposed operators on the decision-making process, Fermatean fuzzy TOPSIS was established.

中文翻译：

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具有dombi聚合算子的Fermatean模糊TOPSIS方法及其在多准则决策中的应用

代数运算可有效地用于决策问题。特别是在决策领域中经常使用Dombi，Hamacher和Einstein代数运算符。另一方面，已知聚合运算符会影响决策问题中的决策过程。在本文中，我们使用Dombi运算来开发一些Fermatean模糊聚合算子。对每种聚合方法进行了算术和几何分析。我们定义了以下算子：Fermatean模糊Dombi加权平均算子，Fermatean模糊Dombi加权几何算子，Fermatean模糊Dombi有序加权平均算子，Fermatean模糊Dombi有序加权几何算子，Fermatean模糊Dombi混合加权平均算子，Fermatean模糊Dombi混合加权算子操作员。也，对Dombi参数的beta值进行了分析。提出了拟算子的性质，并在Fermatean模糊集上定义了算子。最后，将提议的运算符与现有的聚合运算符进行了比较。为了了解拟议的运营商对决策过程的影响，建立了Fermatean Fuzzy TOPSIS。