The idea of rough continuous functions is essential to comprehending the dynamics and structure of data in the field of information systems theory. Within the information systems paradigm, this study examines the connection between rough set theory and continuity. We start by outlining the rough sets' theoretical underpinnings and how they are used in data analysis and display. Building upon this foundation, we introduce the notion of rough continuous functions, which extend traditional continuity concepts to accommodate the ambiguity intrinsic to rough set theory. Key contributions include a formal definition of rough continuous functions and an exploration of their properties within information systems. We investigate how these functions facilitate a more nuanced understanding of data behavior, particularly in scenarios where data exhibit varying degrees of granularity and uncertainty. Practical implications are discussed, highlighting the potential applications of rough continuous functions in data-driven decision-making and information system design. By connecting rough set theory with continuous functions, this paper not only advances theoretical understanding but also offers practical insights into managing and interpreting complex data structures within information systems.