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The intuitionistic fuzzy set, briefly as; IFS and its extension involving Pythagorean fuzzy set (PFS) and Fermatean fuzzy set (FFS), are all effective tools to express uncertain and incomplete cognitive information with membership, nonmembership, and hesitancy degrees. The FFS introduced by Senapati and Yager, carries out uncertain and imprecise information smartly in exercising decision‐making than IFS and PFS. A generalized form of union and intersection on FFS can be formulated from a generalized T‐norm and T‐conorm. Hamacher operations such as Hamacher product and Hamacher sum, are good alternatives to product and sum. In this course of this article, we first device new operations on Fermatean fuzzy information by employing Hamacher T‐conorm and T‐norm and discuss basic operations. Induced by the Hamacher operations and FFS, we propose Fermatean fuzzy Hamacher arithmetic and …