<p>Rough set theory employs approximation techniques to classify objects into indiscernibility classes and serves as an effective tool for analyzing and making decisions under imprecise and uncertain conditions. Intuitionistic fuzzy sets, as an extension of classical fuzzy sets, enrich the representation of complex and ambiguous information by introducing an additional membership function, thereby reducing uncertainty and imprecision in decision-making. By integrating these two concepts, an intuitionistic fuzzy rough framework is developed, offering a more versatile and comprehensive approach for modeling and processing incomplete information in information systems. This study introduces the concept of an intuitionistic fuzzy rough graph and formally defines one of its essential components, the adjacency matrix. The matrix provides a systematic representation of relationships and discernibility among elements by capturing the interconnections between nodes in the graph. Furthermore, based on the adjacency matrix, lower and upper bounds of the energy of an intuitionistic fuzzy rough graph are established, demonstrating their usefulness in decision-making. These bounds serve as analytical measures that help characterize the energy levels associated with different intuitionistic fuzzy rough graph structures. Ultimately, they offer helpful details about the overall behavior and structural properties of such graphs within this mathematical framework. To illustrate its practical relevance, the application-oriented part of this research presents a real-life case study on site selection for school construction using the proposed decision-making method.</p>