<p>Lung cancer remains one of the leading causes of cancer-related mortality worldwide, with early and accurate diagnosis playing a pivotal role in improving patient outcomes. However, the diagnostic process is frequently impeded by inherent uncertainty, vague and overlapping symptomatology, and inconsistencies in expert judgments limitations that conventional decision-making models struggle to adequately address. To bridge this gap, this study proposes a novel fuzzy environment termed the C-HyFS, which synthesizes and extends the expressive capabilities of C-IFSs and HFSs. Unlike existing models, the C-HyFS framework is explicitly designed to model complex uncertainty structures by incorporating both high-circular and hyperbolic information dynamics, enabling greater representational flexibility. Within this novel theoretical setting, we formulate generalized arithmetic operations specifically, addition and multiplication over C-HyFNs, providing the foundational tools required for advanced uncertainty modeling. Furthermore, we introduce a prioritized weighted aggregation operator that integrates decision-makers’ preferences into the evaluation process while preserving robustness and mathematical coherence. Based on these developments, a new MADM method tailored to the C-HyFS context is proposed. This method systematically integrates attribute structures, uncertain data, and preference prioritization, offering a comprehensive framework well suited for complex decision environments. To validate the applicability and effectiveness of the proposed approach, we conduct detailed numerical simulations, including a case study focused on early stage lung cancer screening. The results demonstrate that the proposed method significantly enhances decision accuracy and interpretability, particularly in situations characterized by preference ambiguity and multifaceted uncertainty domains where traditional models often exhibit limited performance.</p>