Interval-valued Fermatean fuzzy sets (IVFFSs) were introduced as a more effective mathematical tool for handling uncertain information in 2021. In this paper, firstly, a novel score function (SCF) is proposed based on IVFFNs that can distinguish between any two IVFFNs. And then, the novel SCF and hybrid weighted score measure were used to construct a new multi-attribute decision-making (MADM) method. Besides, three cases are used to demonstrate that our proposed method can overcome the disadvantages that the existing approaches cannot obtain the preference orderings of alternatives in some circumstances and involves the existence of division by zero error in the decision procedure. Compared with the two existing MADM methods, our proposed approach has the highest recognition index and the lowest error rate of division by zero. Our proposed method provides a better approach to dealing with the MADM problem in the interval-valued Fermatean fuzzy environment.