This article introduces novel definitions for generalized rough-set models, that using the concepts of initial neighborhoods and ideals. A comprehensive examination of the properties inherent in these newly introduced types is provided. A meticulous comparison between the proposed definitions and previously published studies, underscoring the broader applicability of the definitions presented herein. The obtained results and illustrative examples serve to substantiate the claim that the newly proposed method adeptly diminishes boundary regions while concurrently optimizing accuracy. Furthermore, the article establishes initial rough membership functions through ideals, applicable to any binary relation  on a universe , and introduces an innovative approach to lower and upper approximations utilizing the 𝜄-membership function. The exposition includes a compelling medical application to elucidate the determination of exact and rough sets for each technique. Finally, an exhaustive analysis of the dengue fever information system is conducted to validate the efficacy of the proposed approaches in maximizing accuracy and minimizing boundary regions.