<p>Complex Fermatean fuzzy sets (CFFSs) represent an advanced development of fuzzy sets by integrating aspects of complex fuzzy sets and Fermatean fuzzy sets. Such integration facilitates enhanced modeling and depiction of uncertain information within complex environments, surpassing the capabilities of complex intuitionistic and Pythagorean fuzzy sets. Despite these advantages, an urgent challenge is how to accurately evaluate the dissimilarity between CFFSs. Therefore, in this paper, we propose two generalized complex Fermatean fuzzy distance measures for CFFSs as well as their weighted counterparts. Furthermore, we demonstrate some key properties of the proposed distance measures, which illustrate their feasibility and effectiveness. Under certain circumstances, the proposed distance measures can be transformed into a hybrid complex Fermatean Hamming–Hausdorff and Euclidean–Hausdorff distance measures. Building on the proposed distance measures, we present a new entropy measure for CFFS. Finally, we propose a new decision-making method based on the proposed distance and entropy measures and apply the proposed method to lung disease recognition. The experiments demonstrate that the proposed distance measures effectively capture the dissimilarities between diseases represented as CFFSs, with the method achieving accurate classification results.</p>