Complex intuitionistic fuzzy set (CIFS) is a special intuitionistic fuzzy set where the membership and non-membership degrees are expressed by a complex-valued membership degree and can more easily describe the vagueness and uncertainty in the real world. Archimedean t-conorm and t-norm (ATT), as an important class of the t-norm (TN) and t-conorm (TC), have greater flexibility in the information fusion process. In this paper, we extend the ATT to CIFSs and present some generalized geometric aggregation operators, which can be used to handle the multiple criteria decision-making (MCDM) problems. For it, we firstly define some new operational laws of the CIFSs based on ATT, then some weighted geometric aggregation operators based on proposed operations are proposed. Further, some desirable properties and special cases of them are studied. Finally, a decision-making approach is developed for the MCDM problem with complex intuitionistic fuzzy information. A practical example is given to show the availability and advantages of the proposed method by comparison with some existing methods. The proposed aggregation operators are more generalized than the existing ones to utilize the uncertain and imprecise information. Several existing operators are considered as special cases of the proposed one. Finally, the proposed method will offer various choices to the decision-maker to access the finest alternatives.

中文翻译：

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复杂直觉模糊集的基于T-范数运算的广义几何集合算子及其在决策中的应用

复杂直觉模糊集（CIFS）是一种特殊的直觉模糊集，其中隶属度和非隶属度由复数值隶属度表示，可以更轻松地描述现实世界中的模糊性和不确定性。阿基米德t-conorm和t-norm（ATT）作为t-norm（TN）和t-conorm（TC）的重要类别，在信息融合过程中具有更大的灵活性。在本文中，我们将ATT扩展到CIFS，并提出了一些通用的几何聚合算子，可用于处理多准则决策（MCDM）问题。为此，我们首先定义了基于ATT的CIFS的一些新的操作律，然后提出了基于所提出操作的一些加权几何集合算子。此外，研究了一些理想的特性和特殊情况。最后，针对带有复杂直觉模糊信息的MCDM问题，开发了一种决策方法。通过与一些现有方法进行比较，给出了一个实际例子来说明该方法的可用性和优点。所提出的聚合算子比现有算子更通用，以利用不确定和不精确的信息。一些现有的运营商被认为是提议运营商的特殊情况。最后，所提出的方法将为决策者提供各种选择，以获取最佳选择。所提出的聚合算子比现有算子更通用，以利用不确定和不精确的信息。现有的几个运营商被认为是提议运营商的特殊情况。最后，所提出的方法将为决策者提供各种选择，以获取最佳选择。所提出的聚合算子比现有算子更通用，以利用不确定和不精确的信息。现有的几个运营商被认为是提议运营商的特殊情况。最后，所提出的方法将为决策者提供各种选择，以获取最佳选择。