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This article proposes novel cosine and weighted cosine similarity measures based on intuitionistic hesitant fuzzy rough sets and examines their fundamental characteristics. Similarity measures are crucial and advantageous tools that have a broad range of applications in decision making, data mining, medical diagnosis, and pattern recognition. To demonstrate the validity of the proposed similarity measures, an illustrative example in the evaluation of volatile currency in Pakistan is presented to verify the efficacy of our approach. Additionally, the rankings of suggested similarity measures are compared to those identified in the literature. The findings demonstrate that the innovative similarity measures lead in consistent patterns of ranking. The comparison confirms that the suggested similarity measures methodologies may achieve precise classification results and are applicable to real-world challenges involving hesitancy and uncertainty. [ABSTRACT FROM AUTHOR]