Weighted hyperrough set and sequential hyperrough set

Authors

  • Takaaki Fujita * Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan.

https://doi.org/10.48313/uda.vi.74

Abstract

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 upon
these foundational concepts, further generalizations such as Hyperrough Sets and Superhyperrough Sets have been
developed. The Weighted Rough Set is an extension of rough set theory that incorporates importance weights
for attributes, enabling more precise classification and approximation. In this paper, we investigate the Weighted
Hyperrough Set, Weighted Superhyperrough Set, Sequential Hyperrough Set, and Sequential n-Superhyperrough
Set, each of which extends the fundamental ideas of Weighted Rough Sets and Sequential Rough Sets to more
complex and high-dimensional decision environments.

Keywords:

Rough set, Hyperrough set, Weighted rough set, Superhyperrough set

References

  1. [1] Pawlak, Z. (1982). Rough sets. International journal of computer & information sciences, 11, 341–356.
  2. [2] Pawlak, Z., Wong, S. K. M., & Ziarko, W. (1988). Rough sets: Probabilistic versus deterministic approach. International journal of man-machine studies, 29(1), 81-95.
  3. [3] Pawlak, Z., Grzymala-Busse, J., Slowinski, R., & Ziarko, W. (1995). Rough sets. Communications of the ACM, 38(11), 88-95. https://doi.org/10.1145/219717.219791
  4. [4] Jech, T. (2003). Set theory. The third millennium edition, revised and expanded. Springer-Verlag, Berlin. https://doi.org/10.1007/3-540-44761-X
  5. [5] Pawlak, Z. (1998). Rough set theory and its applications to data analysis. Cybernetics & Systems, 29(7), 661-688. https://doi.org/10.1080/019697298125470
  6. [6] Fujita, T. (2025). Short introduction to rough, hyperrough, superhyperrough, treerough. Advancing uncertain combinatorics through graphization, hyperization, and uncertainization: Fuzzy, neutrosophic, soft, rough, and beyond: Fifth volume: Various Super-HyperConcepts (Collected Papers). https://www.researchgate.net/publication/388754283
  7. [7] Fujita, T. (2025). A study on hyperfuzzy hyperrough sets, hyperneutrosophic hyperrough sets, and hypersoft hyperrough sets with applications in cybersecurity. Artificial intelligence in cybersecurity, 2, 14–36. https://doi.org/10.61356/j.aics.2025.2501
  8. [8] Fujita, T. (2024). Hyperrough cubic set and superhyperrough cubic set. Prospects for Applied Mathematics and Data Analysis, 4(1), 28-35. https://doi.org/10.54216/PAMDA.040103
  9. [9] Fujita, T., & Smarandache, F. (2025). A concise introduction to hyperfuzzy, hyperneutrosophic, hyperplithogenic, hypersoft, and hyperrough sets with practical examples. Neutrosophic sets and systems, 80, 610-615.
  10. [10] Fujita, T. (2024). Note for intuitionistic hyperrough set, one–directional s–hyperrough set, tolerance hyperrough set, and dynamic hyperrough set. Soft computing fusion with applications, 2(3), 157-183. https://doi.org/10.22105/scfa.vi.51
  11. [11] Fujita, T. (2025). Advancing uncertain combinatorics through graphization, hyperization, and uncertainization: Fuzzy, neutrosophic, soft, rough, and Beyond. Biblio Publishing. https://www.researchgate.net/publication/386082978
  12. [12] Fujita, T. (2025). Neighborhood hyperrough set and neighborhood superhyperrough set. Pure mathematics for theoretical computer science, 5(1), 34-47. https://www.americaspg.com/article/3834/pdf/stream
  13. [13] Fujita, T. (2025). Expanding the horizons of graph theory: Rough tree-width, hyperrough structures, and superhyperrough generalizations. Applied mathematics on science and engineering, 2(1), 21-35. https://doi.org/10.65036/amse212
  14. [14] Fujita, T. (In Press). Hyperrough topsis method and superhyperrough topsis method. Uncertainty discourse and applications. https://doi.org/10.48313/uda.vi.53
  15. [15] Liu, J., Hu, Q., & Yu, D. (2008). A weighted rough set based method developed for class imbalance learning. Information sciences, 178(4), 1235-1256. https://doi.org/10.1016/j.ins.2007.10.002
  16. [16] Liu, J., Hu, Q., & Yu, D. (2008). A comparative study on rough set based class imbalance learning. Knowledge-Based Systems, 21(8), 753-763. https://doi.org/10.1016/j.knosys.2008.03.031
  17. [17] Alam, S. I., Hassan, S. I., & Uddin, M. (2018). Fuzzy models and business intelligence in web-based applications. In Applications of soft computing for the web (pp. 193-221). Singapore: Springer Singapore. https://doi.org/10.1007/978-981-10-7098-3_12
  18. [18] Sateesh, N., Srinivasa Rao, P., & Rajya Lakshmi, D. (2023). Optimized ensemble learning‐based student's performance prediction with weighted rough set theory enabled feature mining. Concurrency and computation: Practice and experience, 35(7), e7601. https://doi.org/10.1002/cpe.7601
  19. [19] Kumar, S. S., & Inbarani, H. H. (2015). Optimistic multi-granulation rough set based classification for medical diagnosis. Procedia computer science, 47, 374-382. https://doi.org/10.1016/j.procs.2015.03.219
  20. [20] Adlassnig, K. P. (1986). Fuzzy set theory in medical diagnosis. IEEE Transactions on systems, man, and cybernetics, 16(2), 260-265. https://doi.org/10.1109/TSMC.1986.4308946
  21. [21] Thomas, L., Crook, J., & Edelman, D. (2017). Credit scoring and its applications. Society for industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611974560
  22. [22] Abdou, H. A., & Pointon, J. (2011). Credit scoring, statistical techniques and evaluation criteria: A review of the literature. Intelligent systems in accounting, finance and management, 18(2-3), 59-88. https://doi.org/10.1002/isaf.325
  23. [23] Lovett, G. M., Burns, D. A., Driscoll, C. T., Jenkins, J. C., Mitchell, M. J., Rustad, L., ... ., & Haeuber, R. (2007). Who needs environmental monitoring? Frontiers in ecology and the environment, 5(5), 253-260. https://doi.org/10.1890/1540-9295(2007)5[253:WNEM]2.0.CO;2
  24. [24] Artiola, J. F., Pepper, I. L., & Brusseau, M. L. (2004). Environmental monitoring and characterization. Academic Press.
  25. [25] Biber, E. (2013). The problem of environmental monitoring. Envtl. L. Rep. News & Analysis, 43, 10695. https://access.heinonline.com/HOL/LandingPage?handle=hein.journals/elrna43&div=104&id=&page=
  26. [26] Bi, X., Sun, Y., Yang, Y., Lee, A., Hou, D., Liu, B., ... & Hu, N. (2026). Research on piston aeroengine fault diagnosis method with acoustic emission signal and rough set theory synergy. Structural Health Monitoring, 25(2), 1150-1164. https://doi.org/10.1177/14759217241305708
  27. [27] Xu, W., Yan, Y., & Li, X. (2024). Sequential rough set: A conservative extension of Pawlak’s classical rough set: W. Xu et al. Artificial intelligence review, 58(1), 9. https://doi.org/10.1007/s10462-024-10976-z
  28. [28] Asadi, R., Modiri, A., Hosseinali, F., & Gholizadeh, A. A. (2023). A Patterns of housing and neighborhood selection among special groups; A review of housing selection models in Tehran city. Journal of Iranian architecture & urbanism (JIAU), 14(2), 285-299.
  29. [29] Lindstrom, B. (1997). A sense of place: Housing selection on Chicago's North Shore. The sociological quarterly, 38(1), 19-39. https://doi.org/10.1111/j.1533-8525.1997.tb02338.x
  30. [30] Lim, S. M., & Ha, K. S. (2015). The relations of the life style and housing selection attributes of the middle-aged people. Journal of the Korea academia-industrial cooperation society, 16(11), 8074-8088.
  31. [31] Kizielewicz, B., & Bączkiewicz, A. (2021). Comparison of Fuzzy TOPSIS, Fuzzy VIKOR, Fuzzy WASPAS and Fuzzy MMOORA methods in the housing selection problem. Procedia computer science, 192, 4578-4591. https://doi.org/10.1016/j.procs.2021.09.236

Downloads

Published

2026-06-21

Issue

Vol. 3 No. 2 (2026): Uncertainty Discourse and Applications

Section

Articles

How to Cite

Fujita, T. (2026). Weighted hyperrough set and sequential hyperrough set. Uncertainty Discourse and Applications, 3(2), 150-165. https://doi.org/10.48313/uda.vi.74

Similar Articles

1-10 of 32

You may also start an advanced similarity search for this article.