Intuitionistic Fuzzy Z-Contractions and Common Fixed Points with Applications

In the context of $b$-metric spaces, this paper introduces two concepts: admissible hybrid intuitionistic fuzzy $\mathcal{Z}$-contractions and pairwise admissible hybrid intuitionistic fuzzy $\mathcal{Z}$-contractions and establishes criteria for intuitionistic fuzzy fixed points under such contractions. It is demonstrated that a pair of set-valued maps possesses a common fixed point. Various illustrative examples are provided to validate these results. Moreover, the significant implications of our main theorem are explored and analyzed across different types of simulation functions. Furthermore, we derive several fixed point results in the context of partially ordered b-metric spaces, offering insights from an application-oriented perspective. These outcomes extend and generalize several prior results documented in the literature.