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American Scientific Publishing Group

verified Journal

Prospects for Applied Mathematics and Data Analysis

ISSN
Online: 2836-4449
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Continuous publication

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Open access journal. All articles are freely available online with no APC.

Prospects for Applied Mathematics and Data Analysis
Full Length Article

Volume 4Issue 1PP: 28-35 • 2024

HyperRough Cubic Set and SuperhyperRough Cubic Set

Takaaki Fujita 1*
1Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan
* Corresponding Author.
Received: January 28, 2024 Revised: March 27, 2024 Accepted: June 30, 2024

Abstract

Rough sets provide a mathematical framework for approximating subsets using lower and upper bounds determined by equivalence relations, effectively modeling uncertainty in classification and data analysis. These foundational concepts have been further extended to structures such as Hyperrough Sets and Superhyperrough Sets. In this paper, we introduce the definitions of Hyperrough Cubic Sets and Superhyperrough Cubic Sets, and explore their fundamental properties. We hope that these developments will promote further research into applications such as decision-making based on Rough Set Theory and its extensions.

Keywords

Rough set Hyperrough Set Rough Cubic Set SuperHyperRough Set

References

[1] Said Broumi, Florentin Smarandache, and Mamoni Dhar. Rough neutrosophic sets. Infinite Study, 32:493 502, 2014.

[2] Xueyou Chen. On rough cubic sets. Annals of Fuzzy Mathematics and Informatics, 21(3):319–331, 2021.

[3] Yumin Chen, Duoqian Miao, Ruizhi Wang, and Keshou Wu. A rough set approach to feature selection based on power set tree. Knowledge-Based Systems, 24(2):275–281, 2011.

[4] V Chinnadurai, S Thayalan, and A Bobin. Complex cubic set and their properties. Advances in mathematics: Scientific journal, 9(4):1561–1567, 2020.

[5] Takaaki Fujita. Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutro- sophic, Soft, Rough, and Beyond. Biblio Publishing, 2025.

[6] Takaaki Fujita. Hyperfuzzy hyperrough set, hyperneutrosophic hyperrough set, and hypersoft hyperrough set. Preprint, 2025.

[7] Takaaki Fujita. Hyperplithogenic cubic set and superhyperplithogenic cubic set. Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond, page 79, 2025.

[8] Takaaki Fujita. Short introduction to rough, hyperrough, superhyperrough, treerough, and multirough set. Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond: Fifth volume: Various Super-HyperConcepts (Collected Papers), page 394, 2025.

[9] Takaaki Fujita. A study on hyperfuzzy hyperrough sets, hyperneutrosophic hyperrough sets, and hypersoft hyperrough sets with applications in cybersecurity. Artificial Intelligence in Cybersecurity, 2:14–36, 2025.

[10] JG Lee, G Senel, J Kim, DH Yang, and K Hur. Cubic crisp sets and their application to topology. Ann. Fuzzy Math. Inform, 21(3):227–265, 2021.

[11] Zdzisław Pawlak. Rough sets. International journal of computer & information sciences, 11:341–356, 1982.

[12] Zdzislaw Pawlak. Rough set theory and its applications to data analysis. Cybernetics & Systems, 29(7):661 688, 1998.

[13] Zdzisław Pawlak and Andrzej Skowron. Rudiments of rough sets. Information sciences, 177(1):3–27, 2007.

 

[14] Tapan Senapati, Young Bae Jun, and Kar Ping Shum. Cubic set structure applied in up-algebras. Discrete Mathematics, Algorithms and Applications, 10(04):1850049, 2018.

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Fujita, Takaaki. "HyperRough Cubic Set and SuperhyperRough Cubic Set." Prospects for Applied Mathematics and Data Analysis, vol. Volume 4, no. Issue 1, 2024, pp. 28-35. DOI: https://doi.org/10.54216/PAMDA.040103
Fujita, T. (2024). HyperRough Cubic Set and SuperhyperRough Cubic Set. Prospects for Applied Mathematics and Data Analysis, Volume 4(Issue 1), 28-35. DOI: https://doi.org/10.54216/PAMDA.040103
Fujita, Takaaki. "HyperRough Cubic Set and SuperhyperRough Cubic Set." Prospects for Applied Mathematics and Data Analysis Volume 4, no. Issue 1 (2024): 28-35. DOI: https://doi.org/10.54216/PAMDA.040103
Fujita, T. (2024) 'HyperRough Cubic Set and SuperhyperRough Cubic Set', Prospects for Applied Mathematics and Data Analysis, Volume 4(Issue 1), pp. 28-35. DOI: https://doi.org/10.54216/PAMDA.040103
Fujita T. HyperRough Cubic Set and SuperhyperRough Cubic Set. Prospects for Applied Mathematics and Data Analysis. 2024;Volume 4(Issue 1):28-35. DOI: https://doi.org/10.54216/PAMDA.040103
T. Fujita, "HyperRough Cubic Set and SuperhyperRough Cubic Set," Prospects for Applied Mathematics and Data Analysis, vol. Volume 4, no. Issue 1, pp. 28-35, 2024. DOI: https://doi.org/10.54216/PAMDA.040103
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