<p>Interval-valued Fermatean fuzzy sets (IVFFSs) extend Fermatean fuzzy sets by using interval values to improve uncertainty representation. Nevertheless, existing fuzzy reasoning methods lack logical operator foundations in IVFFS environments. To tackle this issue, this study focuses on a similarity-based fuzzy reasoning method oriented towards the IVFFSs-based environment, for handling the problems of fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT) in approximate reasoning. First, an interval-valued Fermatean triangular norm (t-norm) and its residuated interval-valued Fermatean implication are established. Next, a unified representation of residuated interval-valued Fermatean implication is given, revealing their relationship with classical fuzzy implication. On this basis, three expressions of residuated interval-valued Fermatean implications are demonstrated. Subsequently, an interval-valued Fermatean biresiduum-induced similarity measure is discussed. Afterwards, we integrate it with similarity reasoning principle and acquire solutions for the FMP and FMT. The reducibility and robustness of the similarity-based inference algorithm are verified through simulation experiments, which validate both the robustness conclusions and the perturbation-sensitive advantages of our proposed metric. Finally, the effectiveness and superiority of our method are demonstrated via two pattern recognition case studies with comparative experiments.</p>