Political shift from free trade to protectionism and emerging and escalating trade and military conflicts have amplified geopolitical risk, disruptions in global supply chains, and made these threats central to business decisions. Yet, systematic methods to assess and manage such risks remain scarce. To address this gap, we propose a novel fuzzy real options framework under geopolitical risk, integrating managerial adaptability with interval-valued scenarios. While real options theory captures the value of managerial flexibility in volatile, long-term investments, fuzzy modeling accounts for inherent ambiguity and imprecision. Building on the fuzzy root-mean-square (RMS) fuzzy pay-off method for real option valuation, our extended approach, interval RMS-FPOM, utilizes interval-valued trapezoidal fuzzy numbers to enhance risk representation and support decision-making. The method is compared to the center-of-gravity payoff approach, highlighting its advantages in practical application. A numerical example of supply chain disruption risk illustrates how real options, independent or sequential, can be exercised by firms internally or, for instance, through acquisitions to build strategic synergies. This framework provides a robust tool for valuing real options in high-uncertainty environments, such as supply chain networks, enabling more informed decisions under uncertain geopolitical tensions. In practical terms, this framework offers managers a more nuanced tool to evaluate supply chain investments, such as acquiring new facilities or switching suppliers, under the ambiguous and often unquantifiable conditions imposed by geopolitical instability, thereby improving strategic decision-making in volatile global markets.