Fermatean fuzzy (FF) sets, building on the extensions of the foundations laid by intuitionistic and Pythagorean fuzzy sets, have emerged as a highly generalized and adaptable framework for addressing uncertainty in decision-making processes. By incorporating multiple levels of uncertainty, they offer a more flexible approach to modeling imprecise or ambiguous information. This paper introduces two novel distances for FF sets, situated within the context of covering-based rough sets and grounded in robust mathematical proofs. A comparative analysis is also performed between the newly proposed and existing state-of-the-art distances in multi-criteria decision-making, particularly within the impact of fuzzy \(\sigma \) -neighborhoods. The experimental results reveal a notable similarity in decision-making outcomes across the various distances, leading to their classification into several distinct equivalence classes.