Sun Bingzhen, Tong Sirong, Ma Weimin, Wang Ting, Jiang Chao
School of Economics and Management, Xidian University, Xi'an, 710071 China.
School of Economics and Management, Tongji University, Shanghai, 200092 China.
Artif Intell Rev. 2022;55(3):1887-1913. doi: 10.1007/s10462-021-10048-6. Epub 2021 Aug 6.
Exploring efficiency approaches to solve the problems of decision making under uncertainty is a mainstream direction. This article explores the rough approximation of the uncertainty information with Pythagorean fuzzy information on multi-granularity space over two universes combined with grey relational analysis. Based on grey relational analysis, we present a new approach to calculate the relative degree or the attribute weight with Pythagorean fuzzy set and give a new descriptions for membership degree and non-membership. Then, this paper proposes a multi-granulation rough sets combined with Pythagorean fuzzy set, including optimistic multi-granulation Pythagorean fuzzy rough set, pessimistic multi-granulation Pythagorean fuzzy rough set and variable precision Pythagorean fuzzy rough set. Several basic properties for the established models are investigated in detail. Meanwhile, we present an approach to solving the multiple-criteria group decision making problems with fuzzy information based on the proposed model. Eventually, a case study of psychological evaluation of health care workers in COVID-19 show the principle of the established model and is utilized to verify the availability. The main contributions have three aspects. The first contribution of an approach of calculating the attribute weight is presented based on Grey Relational Analysis and gives a new perspective for the Pythagorean fuzzy set. Then, this paper proposes a mutli-granulation rough set model with Pythagorean fuzzy set over two universes. Finally, we apply the proposed model to solving the psychological evaluation problems.
探索解决不确定性下决策问题的效率方法是一个主流方向。本文结合灰色关联分析，研究了在两个论域的多粒度空间上用毕达哥拉斯模糊信息对不确定性信息进行粗糙近似。基于灰色关联分析，提出了一种用毕达哥拉斯模糊集计算相对度或属性权重的新方法，并对隶属度和非隶属度给出了新的描述。然后，本文提出了一种结合毕达哥拉斯模糊集的多粒度粗糙集，包括乐观多粒度毕达哥拉斯模糊粗糙集、悲观多粒度毕达哥拉斯模糊粗糙集和变精度毕达哥拉斯模糊粗糙集。详细研究了所建立模型的几个基本性质。同时，基于所提出的模型，给出了一种解决模糊信息下多准则群决策问题的方法。最后，通过对新冠肺炎医护人员心理评估的案例研究，展示了所建立模型的原理，并验证了其有效性。主要贡献有三个方面。一是基于灰色关联分析提出了一种计算属性权重的方法，为毕达哥拉斯模糊集提供了一个新的视角。二是提出了一种在两个论域上基于毕达哥拉斯模糊集的多粒度粗糙集模型。最后，将所提出的模型应用于解决心理评估问题。
