Graded HyperRough Set and Linguistic HyperRough Set
Takaaki Fujita1,∗, Arif Mehmood2
1Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan
2Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050,
KPK, Pakistan
Emails: Takaaki.fujita060@gmail.com; mehdaniyal@gmail.com
Abstract
Numerous mathematical frameworks have been developed to handle uncertainty, including Fuzzy Sets,1 In-
tuitionistic Fuzzy Sets,2 Hyperfuzzy Sets,3 Picture Fuzzy Sets,4 Hesitant Fuzzy Sets,5, 6 Neutrosophic Sets,7
Plithogenic Sets,8 and Soft Sets,9 and research in this area continues to evolve rapidly. Rough set theory
provides a foundational method for approximating subsets using lower and upper bounds based on equiva-
lence relations, offering an effective approach to modeling uncertainty in classification and data analysis.10, 11
Building upon these foundations, extended models such as HyperRough Sets and SuperHyperRough Sets have
been proposed.12 In this paper, we present novel definitions that further generalize Graded Rough Sets and
Linguistic Rough Sets—specifically, the Graded HyperRough Set and the Linguistic HyperRough Set. These
new frameworks are expected to contribute to the advancement of research in fields such as decision-making,
language theory, and artificial intelligence.
Keywords: Rough set; Hyperrough Set; Linguistic Rough Set; SuperHyperRough set; Graded Rough Set