(untitled) (European Journal of Pure and Applied Mathematics, 2024)
This paper introduces a pioneering advancement in rough set theory by presenting a new class of rough sets termed h-rough sets. Central to this novel approach are the concepts of h-lower and h-upper approximations, intricately tied to the notion of h-open sets. We delve into the fundamental properties of h-rough sets and establish the framework of h-approximation spaces, offering a comprehensive understanding of their theoretical underpinnings. Moreover, we introduce and rigorously analyze the concepts of h-rough equality and h-rough inclusion, providing formal definitions and insightful examinations of their implications in data approximation tasks. Through detailed examples and thorough exploration, this paper showcases how h-rough sets extend rough set theory, offering more flexible and precise techniques for data approximation. This study not only contributes to the theoretical development of rough set theory but also opens up exciting possibilities for practical applications across various domains.