Neighborhood HyperRough Set and Neighborhood SuperHyperRough

Set

Takaaki Fujita 1,∗

1Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan

Email: takaaki.fujita060@gmail.com

Abstract

Fuzzy sets,20 rough sets,14 intuitionistic fuzzy sets,3 neutrosophic sets,15 soft sets,13 hesitant fuzzy set,17

plithogenic sets,16 and other uncertainty-handling frameworks have been the focus of intensive and ongoing

research. Rough set theory provides a mathematical framework for approximating subsets through lower and

upper approximations defined by equivalence relations, effectively capturing uncertainty in classification and

data analysis.5, 10 Building upon these foundational concepts, further generalizations such as Hyperrough Sets8

and Superhyperrough Sets have been introduced. In this paper, we investigate the concepts of Neighborhood

Hyperrough Sets and Neighborhood Superhyperrough Sets. These models extend the classical Neighborhood

Rough Set framework by incorporating the structural richness of Hyperrough Sets and Superhyperrough Sets.

Keywords: Rough set; Hyperrough Set; Neighborhood Rough Set; SuperHyperRough set