Li Jinjun, Chen Minghao, Pei Shibing
School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024 Liaoning China.
Artif Intell Rev. 2023 Jan 18:1-54. doi: 10.1007/s10462-022-10376-1.
In this paper, we establish a novel -rung orthopair fuzzy (-ROF) multi-attribute decision making (MADM) model on the basis of the proposed -ROF interactive Hamacher weighted adjustable power average (-ROFIHWAPA) and -ROF interactive Hamacher weighted coordinated Heronian means (HMs), which (1) can reflect the correlations among multiple attributes; (2) weakens the impacts of the extreme evaluation values more reasonably; (3) considers the interactions between the membership degree (MD) and non-membership degree (N-MD) of different -ROF numbers (-ROFNs); (4) has the characteristic of generality (It can generate different methods by different operations). Firstly, the -ROF interactive Hamacher operations, improved score function and new -ROF entropy (-ROFE) formula, which are the necessary raw materials for the implementation of MADM, are presented. Secondly, we introduce the adjustable power average (APA) and its weight form (WAPA) to remedy the deficiencies of the classical power averages (PAs). Afterwards we extend the WAPA to -ROF circumstance and propose the -ROF interactive Hamacher WAPA (-ROFIHWAPA), and its basic properties are analyzed. Further, the entropy weight fitting method is presented to determine the parameter carried by the -ROFIHWAPA. Thirdly, inspired by the evolutionary process of Bonferroni means (BMs), we define the weighted coordinated HM (WCHM) and weighted geometric coordinated HM (WGCHM) based on the traditional HMs, respectively, which eliminate the redundancy of the dual generalized weighted BM (DGWBM) and dual generalized weighted Bonferroni geometric mean (DGWBGM), i.e., the case of Then we develop the -ROF interactive Hamacher WCHM (-ROFIHWCHM) and -ROF interactive Hamacher WGCHM (-ROFIHWGCHM) by combining them with the -ROF interactive Hamacher operations, and the common properties and special cases are also investigated. Finally, we create a MADM algorithm relied on the -ROFIHWAPA and -ROFIHWCHM (resp. -ROFIHWGCHM), and a practical example is introduced to illustrate the effectiveness and superiority of the proposed method.
在本文中，我们基于所提出的-rung正交对模糊（-ROF）交互式哈马赫加权可调幂平均（-ROFIHWAPA）和-ROF交互式哈马赫加权协调赫伦均值（HMs），建立了一种新颖的-rung正交对模糊（-ROF）多属性决策（MADM）模型，该模型（1）能够反映多个属性之间的相关性；（2）更合理地削弱极端评价值的影响；（3）考虑了不同-rung正交对模糊数（-ROFNs）的隶属度（MD）和非隶属度（N-MD）之间的相互作用；（4）具有通用性特征（通过不同运算可生成不同方法）。首先，给出了-ROF交互式哈马赫运算、改进的得分函数和新的-ROF熵（-ROFE）公式，这些是实施MADM的必要原材料。其次，引入可调幂平均（APA）及其权重形式（WAPA）来弥补经典幂平均（PAs）的不足。之后将WAPA扩展到-ROF情形并提出-ROF交互式哈马赫WAPA（-ROFIHWAPA），并分析了其基本性质。进一步，提出熵权拟合方法来确定-ROFIHWAPA所携带的参数。第三，受邦费罗尼均值（BMs）演化过程的启发，分别基于传统HMs定义了加权协调HM（WCHM）和加权几何协调HM（WGCHM），它们消除了对偶广义加权BM（DGWBM）和对偶广义加权邦费罗尼几何均值（DGWBGM）的冗余性，即情况 然后将它们与-ROF交互式哈马赫运算相结合，开发出-ROF交互式哈马赫WCHM（-ROFIHWCHM）和-ROF交互式哈马赫WGCHM（-ROFIHWGCHM），并研究了它们的共同性质和特殊情况。最后，创建了一种基于-ROFIHWAPA和-ROFIHWCHM（分别为-ROFIHWGCHM）的MADM算法，并通过一个实例说明了所提方法的有效性和优越性。
