This study advances both the theoretical and practical aspects of θβ-ideal approximation spaces by refining definitions, introducing- new results, and proposing a comprehensive algorithm for real-world applications. By systematically addressing inaccuracies in previous formulations, we reinforce the foundational principles of θβ-ideal rough set models, ensuring greater consistency and scientific rigor while offering essential complementary results. Furthermore, our approach generalizes existing methodologies, including those developed by Abd El-Monsef et al. (2014) and M. Hosny (2020), thereby enhancing both accuracy and applicability. The proposed mathematical algorithm offers a robust computational framework adaptable to various domains, such as medicine, chemistry, and economics, facilitating improved decision-making processes. These contributions establish a stronger theoretical foundation while expanding the practical relevance of θβ-ideal approximation spaces