Quantum resource theories (QRTs) provide a versatile framework for quantifying and manipulating quantum resources, with widespread applications in quantum communication, computation, and information processing. While the \(\epsilon \) -D version of resource measures has been previously studied, its applicability has been largely restricted to addressing experimental imperfections. To tackle broader challenges such as adversarial interference and probabilistic noise, this paper introduces three novel approaches: the \(\delta \) - \(\mathcal {T}\) version and two weighted integral versions. These measures extend the robustness framework of QRTs, enabling a more comprehensive evaluation of quantum resource resilience under realistic conditions. We rigorously analyze their theoretical properties, including non-negativity, monotonicity, convexity, asymptotic continuity, and monogamy, demonstrating their robustness and versatility. As applications to resource dilution protocols, we establish these measures as fundamental lower bounds for resource costs, showcasing their practical relevance in the design of resilient quantum protocols. This work provides fresh insights into resource quantification within QRTs and offers strong theoretical support for secure and reliable quantum communication and computation protocols.
