Disc intuitionistic fuzzy sets (D-IFSs) offer a generalization of intuitionistic fuzzy sets and circular intuitionistic fuzzy sets (C-IFSs) by introducing a flexible radius function. Unlike C-IFSs where the radius remains constant, D-IFSs allow the radius degree to vary, thereby providing a more nuanced and precise way to model uncertainty in membership and non-membership degrees. This study defines the axioms of disc intuitionistic fuzzy similarity measures, which play a key role in assessing similarity between D-IFSs, and introduces two disc intuitionistic fuzzy similarity measures. Furthermore, a classification algorithm designed for the disc intuitionistic fuzzy environment is proposed. To validate the practicality and effectiveness of the proposed methods, the similarity measures and the classification algorithm are applied to the well-known Iris plant dataset. Experimental results are reported using several key performance metrics, including average accuracy, precision, recall, and F1 score. The findings demonstrate that the proposed approach achieves high classification performance and showcases the advantages of using D-IFSs for handling uncertainty in real-world classification tasks.