Categories of ℒℱ-Rough Topogenous Spaces and ℒℱ-Rough Interior Spaces

This paper aims to present the concepts of [Formula: see text] rough topogenous spaces, where [Formula: see text] is a frame and [Formula: see text] refers to fuzzy sets. We study the relationships among [Formula: see text]-topogenous structures and Čech [Formula: see text]-rough interior spaces. We also establish concrete functors between categories of [Formula: see text]-rough interior spaces and [Formula: see text]-topogenous spaces, which confirms the existence of a Galois correspondence between these spaces. Finally, practical examples within the scope of medicine and information systems are provided to illustrate the applicability of the presented framework under the theory of fuzzy sets.