Liu Peide, Li Dengfeng
School of Economics and Management, Fuzhou University, Fuzhou, Fujian, China.
School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, Shandong, China.
PLoS One. 2017 Jan 19;12(1):e0168767. doi: 10.1371/journal.pone.0168767. eCollection 2017.
Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. Besides, it is a universal operator since it can contain other general operators by assigning some special parameter values. However, the MM can only process the crisp numbers. Inspired by the MM' advantages, the aim of this paper is to extend MM to process the intuitionistic fuzzy numbers (IFNs) and then to solve the multi-attribute group decision making (MAGDM) problems. Firstly, we develop some intuitionistic fuzzy Muirhead mean (IFMM) operators by extending MM to intuitionistic fuzzy information. Then, we prove some properties and discuss some special cases with respect to the parameter vector. Moreover, we present two new methods to deal with MAGDM problems with the intuitionistic fuzzy information based on the proposed MM operators. Finally, we verify the validity and reliability of our methods by using an application example, and analyze the advantages of our methods by comparing with other existing methods.
缪尔黑德均值（MM）是一种著名的聚合算子，它可以考虑由变量向量分配的任意数量的论据之间的相互关系。此外，它是一个通用算子，因为通过分配一些特殊的参数值，它可以包含其他一般算子。然而，MM只能处理清晰数。受MM优点的启发，本文的目的是将MM扩展到处理直觉模糊数（IFN），进而解决多属性群体决策（MAGDM）问题。首先，我们通过将MM扩展到直觉模糊信息来开发一些直觉模糊缪尔黑德均值（IFMM）算子。然后，我们证明了一些性质，并讨论了关于参数向量的一些特殊情况。此外，我们提出了两种基于所提出的MM算子处理具有直觉模糊信息的MAGDM问题的新方法。最后，我们通过一个应用实例验证了我们方法的有效性和可靠性，并通过与其他现有方法的比较分析了我们方法的优点。
