<p>As an extension of Intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs), Fermatean fuzzy sets (FFSs) can express the characteristics of uncertain information more flexibly and accurately. In Fermatean fuzzy sets, effectively measuring the differences between them is an extremely challenging task. Although some distance measures based on Fermatean fuzzy sets have been proposed, they still have some problems in specific scenarios, which may produce counterintuitive or unreasonable results. To further explore this subject, in this paper, inspired by Jensen–Shannon (JS) divergence within probability distribution, two novel distance measures based on Fermatean fuzzy sets have been proposed, the first one takes into account the degree of membership and non-membership, while the second one also incorporates the degree of hesitation. Several properties of these measures are analyzed, and their normalized and weighted versions are also further constructed. Finally, a novel decision-making algorithm is developed based on the proposed distance measures and applied to pattern recognition and medical diagnosis, followed by a comparative analysis with existing methods to demonstrate the effectiveness and potential of the proposed approach.</p>