Note for Intuitionistic HyperRough Set, One–directional S–Hyperrough Set, Tolerance Hyperrough Set,and Dynamic Hyperrough Set

Abstract

Various set-theoretic models have been proposed to handle uncertainty, including Fuzzy Sets, Intuitionistic Fuzzy Sets, Neutrosophic Sets, and Soft Sets.  Rough set theory provides a mathematical framework for approximating subsets using lower and upper bounds defined by equivalence relations, effectively capturing uncertainty in classification and data analysis. Building on these foundational ideas, further generalizations such as Hyperrough Sets and Superhyperrough Sets have been developed.  
In this paper, we introduce newly defined concepts of the Intuitionistic Hyperrough Set, One–directional S–Hyperrough Set, Tolerance Hyperrough Set, and Dynamic Hyperrough Set. These are extended versions of the Intuitionistic Rough Set, One–directional S–rough Set, Tolerance Rough Set, and Dynamic Rough Set, respectively, constructed using the framework of Hyperrough Sets. Additionally, we explore extensions constructed using the Superhyperrough Set framework.