The Fermatean fuzzy set concept, which was developed by merging Fermatean fuzzy sets with hesitant fuzzy sets, may be utilized in practice to ease the solution of complex multi-criteria decision-making (MCDM) issues. The idea of a Fermatean hesitant fuzzy set is introduced first, followed by the operations associated with this concept. Aggregation operations based on Fermatean hesitant fuzzy sets are provided, and their fundamental features are investigated. A novel MCDM approach obtained using operators has been developed to choose the best choice in practice. Finally, the efficiency of the recommended strategies was demonstrated using a lung cancer case study.