In this paper, we considered the defined intuitionistic fuzzy numbers (IFNs) on real numbers and proposed a new method based on Hamacher operators to operate with membership and non-membership degrees of the given IFN in aggregation process. Also, a new method will be introduced to compute the distance between IFNs. These methods will be applied to solve multi-attribute group decision-making (MAGDM) problems, in which IFNs were used to model the arising uncertainty from human judgments or assessments. To do it, Choquet integral, as a powerful tool in both independent and interactive criteria, will be used individually or as a tool to provide appropriate conditions for application of TOPSIS method. The applicability of these methods is illustrated by numerical examples.

在本文中，我们考虑了在实数上定义的直觉模糊数（IFN），并提出了一种基于Hamacher算子的新方法，用于在聚合过程中处理给定IFN的隶属度和非隶属度。而且，将引入一种新方法来计算IFN之间的距离。这些方法将用于解决多属性小组决策（MAGDM）问题，其中使用干扰素（IFN）来建模由人类判断或评估引起的不确定性。为此，Choquet积分既可以作为独立准则也可以作为交互式准则的有力工具，将单独使用或作为为TOPSIS方法应用提供适当条件的工具。数值示例说明了这些方法的适用性。