Intuitionistic fuzzy sets (IFSs) extend fuzzy sets, and they provide a more accurate representation of uncertainty in realistic scenarios. Fuzzy implication operators play a crucial role in fuzzy reasoning. Accordingly, this paper introduces fuzzy implication operators \(\theta \) and \(\theta ^*\) to IFSs, and it correspondingly proposes two types of intuitionistic fuzzy matrix composite operations, where the \((\theta \) , \(\theta ^*)\) induction is comparatively accompanied with a direct formulation from \((\wedge , \vee )\) . Firstly, we investigate concrete properties of fuzzy implication operators \(\theta , \theta ^*\) . Then, two IFSs matrix composite operations are proposed, respectively from \((\wedge , \vee )\) and \((\theta \) , \(\theta ^*)\) . Finally, the two composite operations of IFSs matrices are applied to medical diagnosis, and their application feasibility is verified through a practical medical example; by comparative analyses, the \((\theta , \theta ^*)\) -driven operation better provides right diagnosis results in contrast to previous studies. This study resorts to specific fuzzy implication operators to enrich theoretical research and practical applications of IFSs.