School of Economics and Management, Changzhou Institute of Technology, Changzhou 213032, China.
Comput Intell Neurosci. 2022 May 14;2022:6925670. doi: 10.1155/2022/6925670. eCollection 2022.
As an extension of intuitionistic fuzzy sets (IFSs), picture fuzzy sets (PFSs) can better model and represent the hesitancy and uncertainty of decision makers' preference information. In this study, we propose a multicriteria group decision making (MCGMD) method based on picture fuzzy sets. We first define some basic picture Einstein operations with closed properties among PFSs on the basis of the Einstein t-norms and t-conorms. Then, utilizing the hybrid-weighted operator and the developed picture Einstein operations laws, we put forward a picture fuzzy Einstein hybrid-weighted aggregation operator for aggregating PFSs and discuss its several important properties. Furthermore, we present a new MCGMD method based on the proposed picture fuzzy Einstein hybrid-weighted aggregation operator. Finally, an example is conducted to validate the effectiveness of the proposed MCGMD method.
作为直觉模糊集（IFS）的扩展，图像模糊集（PFS）可以更好地对决策者偏好信息的犹豫和不确定性进行建模和表示。在本研究中，我们提出了一种基于图像模糊集的多准则群体决策（MCGMD）方法。我们首先基于 Einstein t-范数和 t-模定义了一些具有闭合性质的图像 Einstein 运算。然后，利用混合加权算子和开发的图像 Einstein 运算定律，提出了一种用于聚合 PFS 的图像模糊 Einstein 混合加权聚合算子，并讨论了其几个重要性质。此外，我们提出了一种基于所提出的图像模糊 Einstein 混合加权聚合算子的新的 MCGMD 方法。最后，通过一个实例验证了所提出的 MCGMD 方法的有效性。
