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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 4

Topological structures in rough set theory: A survey

Pankaj Kumar Singh
Surabhi Tiwari
Sayfa
1270–1294
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

This study highlights the interdependencies of topology and classical rough set theory and the significant work done in this area during the last twenty years.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Rough set theory provides a mathematical tool to study vague, imprecise, inconsistent and uncertain knowledge.
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Temel Bulgular & Veri:The topological notions are closely related to the notions and results of rough set theory, so the conjoint study of rough set theory and topology becomes essential.
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Sonuç & Katkı:This study highlights the interdependencies of topology and classical rough set theory and the significant work done in this area during the last twenty years.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:rough sets · topological spaces · dynamical systems

Abstract

Rough set theory provides a mathematical tool to study vague, imprecise, inconsistent and uncertain knowledge. The topological notions are closely related to the notions and results of rough set theory, so the conjoint study of rough set theory and topology becomes essential. Researchers have widely discussed the topological aspects and their applications in rough set theory. This study highlights the interdependencies of topology and classical rough set theory and the significant work done in this area during the last twenty years.

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Bu Makaleye Atıf Yap

Singh, P. K., Tiwari, S. (2022). Topological structures in rough set theory: A survey. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 4, 1270–1294. https://ajindex.com/articles/530039

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Kaynakça (19)

  1. F.G. Arenas, Alexandroff spaces, Acta Math. Univ. Comenian. 68, 17–25, 1999
  2. M. Banerjee and M.K. Chakraborty, Rough Consequence and Rough Algebra, in: Rough Sets, Fuzzy Sets and Knowledge Discovery, Proceedings of the International Workshop on Procedings of Rough Sets and Knowledge Discovery, (RSKD’93), Banff, Alberta, Canada, 1993, W.P. Ziarko, (Ed.), Springer Verlag, London, 196–207, 1994
  3. M. Barr and C. Wells, Toposes, Triples and Theories, Springer-Verlag, 1985
  4. W. Bartol, J. Miro, K. Pioro, and F. Rossello, On the coverings by tolerance classes, Inform. Sci. 166 (1-4), 193–211, 2004
  5. G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Publ. 25, 1973
  6. R. Biswas, Rough metric spaces, Bull. Pour. Les. Sous. Ens. Flous. Appl.(France) 68, 21–32, 1996
  7. J. Dai, S. Gao, and G. Zheng, Generalized rough set models determined by multiple neighborhoods generated from a similarity relation, Soft Comput. 13, 2081–2094, 2013
  8. J.P. Doignon and J.C. Falmagne, Knowledge Spaces, Springer, Heidelberg, 1999
  9. A. Dvurecenskij and S. Pulmannova, New trends in quantum structures, Springer Science and Business Media, 2013
  10. P. Eklund, M.A. Galán, and W. Gahler, Partially ordered monads for monadic topologies, Rough Sets and Kleene Algebras, Elect. Notes Theoret. Comp. Sci. 225, 67–81, 2009
  11. B. Ganter and R. Wille, Formal Concept Analysis: Mathematical Foundations, Springer Science and Business Media, 2012
  12. F. Geerts and B. Kuijpers, Topological formulation of termination properties of iterates of functions, Inform. Process. Lett. 89 (1), 31–35, 2004
  13. M.A. Hajri, K. Belaid, and L.J. Belaid, Scattered spaces, compactification and an application to image classification problem, Tatra Mt. Math. Publ. 66 (1), 1–12, 2016
  14. P.C. Hammer, Extended topology: Structure of isotonic functions, J. Reine Angew. Math. 213, 174–186, 1964
  15. T. Herawan, Roughness of sets involving dependency of attributes in information systems, Int J. Softw. Eng. Appl. 9 (7), 111–126, 2015
  16. J.R. Isbell, Uniform Space, in: Math. Surveys Monogr No. 12, Amer. Math. Soc., 1964
  17. J. Järvinen, Approximations and rough sets based on tolerances, in: Lecture Notes in Comput. Sci. 2005, 182–189, Springer-Verlag, Heidelberg, 2001
  18. J. Järvinen, On the structure of rough approximations, Fund. Inform. 53, 135-153, 2002
  19. J. Järvinen, The ordered set of rough sets, in: Lecture Notes in Comput. Sci. 3066, 49–58, Springer-Verlag, Berlin, Heidelb