IEEE Trans Cybern. 2017 Sep;47(9):2514-2530. doi: 10.1109/TCYB.2016.2634599. Epub 2016 Dec 16.
Archimedean t -conorm and t -norm provide the general operational rules for intuitionistic fuzzy numbers (IFNs). The aggregation operators based on them can generalize most of the existing aggregation operators. At the same time, the Heronian mean (HM) has a significant advantage of considering interrelationships between the attributes. Therefore, it is very necessary to extend the HM based on IFNs and to construct intuitionistic fuzzy HM operators based on the Archimedean t -conorm and t -norm. In this paper, we first discuss intuitionistic fuzzy operational rules based on the Archimedean t -conorm and t -norm. Then, we propose the intuitionistic fuzzy Archimedean Heronian aggregation (IFAHA) operator and the intuitionistic fuzzy weight Archimedean Heronian aggregation (IFWAHA) operator. We also further discuss some properties and some special cases of these new operators. Moreover, we also propose a new multiple attribute group decision making (MAGDM) method based on the proposed IFAHA operator and the proposed IFWAHA operator. Finally, we use an illustrative example to show the MAGDM processes and to illustrate the effectiveness of the developed method.
阿基米德 t-范数和 t-范数为直觉模糊数（IFN）提供了一般的运算规则。基于它们的聚合算子可以推广大多数现有的聚合算子。同时，Heronian 均值（HM）具有考虑属性之间相互关系的显著优势。因此，非常有必要基于 IFNs 扩展 HM，并基于阿基米德 t-范数和 t-范数构建直觉模糊 HM 算子。在本文中，我们首先讨论了基于阿基米德 t-范数和 t-范数的直觉模糊运算规则。然后，我们提出了直觉模糊阿基米德 Heronian 聚合（IFAHA）算子和直觉模糊权值阿基米德 Heronian 聚合（IFWAHA）算子。我们还进一步讨论了这些新算子的一些性质和一些特殊情况。此外，我们还提出了一种基于所提出的 IFAHA 算子和 IFWAHA 算子的新的多属性群决策方法（MAGDM）。最后，我们使用一个实例来说明 MAGDM 过程，并说明所提出方法的有效性。
