3-D Golden Rule Representative Value in Decision-Making Systems

Since the authors in Yager (2015), Yager (2018), Dong et al. (2017), and Gao et al. (2021) proposed the concept of golden rule representative value (GRRV) for intervals ranking, some scholars have conducted research in this area. To the best of the author's knowledge, all existing studies on GRRV have utilized a 2-D framework. However, in the current complex decision-making environment, information is presented in various forms, which poses limitations on traditional GRRV architectures. To address the problem, this article proposes two 3-D GRRV structures, which are then applied to two domains: ranking vectors composed of intervals and determining the weights of experts in social network multicriteria group decision-making. In the first GRRV, we propose eight rules that consider the expectation degree, standard deviation, and skewness. In addition, we propose another GRRV considering the expectation degree, uncertainty degree, and centrality degree in the social network. By employing the Takagi, Sugeno, and Kang fuzzy model, we obtain the final representative values. The effectiveness of the proposed methods is validated through a series of examples. Furthermore, comparative analysis with other methods further demonstrates the superiority of our proposed methods.