Fact-checking news claims often encounters situations beyond simple true/false verdicts, involving partial truths, conflicting evidence, or insufficient information. Conventional binary or multi-class rating systems in both manual and automated fact-checking struggle to adequately represent this nuanced reality, particularly the degree and nature of indeterminacy. This paper proposes a novel framework grounded in neutrosophic logic to quantify truth, falsehood, and particularly indeterminacy in automated fact-checking outcomes. Neutrosophy explicitly models information using independent degrees of Truth (T), Indeterminacy (I), and Falsity (F), offering a richer representation than traditional logics. 'Indeterminacy' here encompasses ambiguity, vagueness, contradiction, uncertainty, and neutrality. Based on a systematic literature review spanning journalism, misinformation studies, and uncertainty modeling, we develop a theoretical model and outline a computational procedure for deriving (T, I, F) scores for news claims based on aggregated supporting, refuting, and unresolved evidence identified by automated systems. This approach allows claims to be assessed not just as true or false, but by how true, how false, and how indeterminate they are, given the available evidence, explicitly handling partial truths and contradictions. While primarily theoretical at this stage, the proposed framework offers a foundation for developing more transparent and nuanced AI fact-checking tools capable of communicating the inherent complexities and uncertainties in assessing real-world information, bridging neutrosophic theory with journalistic practice.