Enhancing Complex Decision-Making Under Uncertainty: Theory and Applications of q-Rung Neutrosophic Fuzzy Sets

This thesis pioneers the development of q-Rung Neutrosophic Fuzzy Rough Sets (q-RNFRSs), establishing the first theoretical framework that integrates q-Rung Neutrosophic Sets with rough approximations to break through the conventional μq+ηq+νq≤1 constraint of existing fuzzy–rough hybrids, achieving unprecedented capability in extreme uncertainty representation through our generalized model (Tq+Iq+Fq≤3). The work makes three fundamental contributions: (1) theoretical innovation through complete algebraic characterization of q-RNFRSs, including two distinct union/intersection operations and four novel classes of complement operators (with Theorem 1 verifying their involution properties via De Morgan’s Laws); (2) clinical breakthrough via a domain-independent medical decision algorithm featuring dynamic q-adaptation (q = 2–4) for criterion-specific uncertainty handling, demonstrating 90% diagnostic accuracy in validation trials—a 22% improvement over static models (p<0.001); and (3) practical impact through multi-dimensional uncertainty modeling (truth–indeterminacy–falsity), robust therapy prioritization under data incompleteness, and computationally efficient approximations for real-world clinical deployment.