Note of IndertermRough Set and IndetermHyperRough Set

Various frameworks have been proposed to address uncertainty, including Fuzzy Sets, Intuitionistic Fuzzy Sets, Picture Fuzzy Sets, Vague Sets, and Neutrosophic Sets. A Rough Set approximates uncertain or vague information by means of lower and upper bounds defined via equivalence classes within a universe. Rough Sets have been extensively studied in applications such as decision-making and machine learning. Another prominent approach to modeling uncertainty is the Soft Set, which has been extended in various directions—including the IndetermSoft Set and the IndetermHyperSoft Set—to capture indeterminate information. In this paper, we define and investigate the mathematical structures of IndetermRough Sets and IndetermHyperRough Sets, which generalize the classical Rough Set framework by incorporating indeterminacy into both relations and membership.