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20261017074824
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American Scientific Publishing Group
Galoitica: Journal of Mathematical Structures and Applications
GJMSA
2834-5568
2025
12
2
Graded HyperRough Set and Linguistic HyperRough Set
Takaaki
Fujita
Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan
Arif
Mehmood
Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050, KPK, Pakistan
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Numerous mathematical frameworks have been developed to handle uncertainty, including Fuzzy Sets,1 Intuitionistic 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 equivalence 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.
2025
01
23
4086
https://creativecommons.org/licenses/by/4.0/
10.54216/GJMSA.120201
https://americaspg.com/journal/33/article/4086
-
https://americaspg.com/storage/21757528526.pdf