In this paper, we firstly study two pairs of covering-based fuzzy rough set models and propose the TOPSIS-WAA method based on a covering-based fuzzy rough set. Subsequently, we design a rating scheme based on a multi-criteria decision-making method in a finite fuzzy covering approximation space. The rating scheme is implemented based on the preset subjective ratio and the calculated objective ranking of all alternatives. Furthermore, we use the relevant data of some customers of Industrial and Commercial Bank of China (ICBC) to illustrate the feasibility of our method. At the same time, two test rules are used to verify the validity of the proposed method. Moreover, we compare five different decision-making methods with our method to demonstrate the superiority of our method. Finally, the performance of our method is verified from the perspectives of the best alternative and the optimal ranking.