We propose the cosine similarity measures for intuitionistic fuzzy linguistic sets (IFLSs) and interval‐valued intuitionistic fuzzy linguistic sets (IVIFLSs), which are expressed by the linguistic scale function based on the cosine function. Then, the weighted cosine similarity measure and the ordered weighted cosine similarity measure for IFLSs and IVIFLSs are introduced by taking into account the importance of each element, and the properties of the cosine similarity measures are also given. The main advantage of the proposed cosine similarity measures is that the decision‐makers can flexibly select the linguistic scale function depending on the actual semantic situation. Finally, we present the application of the cosine similarity measures for intuitionistic fuzzy linguistic term sets and interval‐valued intuitionistic fuzzy linguistic term sets to pattern recognition and medical diagnosis, and the existing cosine similarity measures are compared with the proposed cosine similarity measures by the illustrative example.