Review
BibTex RIS Cite

Topological Structure of Pawlak Approximation Spaces and Generalized Rough Sets

Year 2018, Volume: 9 Issue: Ek (Suppl.) 1, 305 - 315, 14.12.2018
https://doi.org/10.29048/makufebed.444556

Abstract

The rough set theory is based on the foundation information systems. The
structure of information systems is closely related to the equivalence
relation, which is a special type of relation in mathematical sense. Rough set
approximation is concerned with imperfect or vague information and taking the
fundamental science center, which uses mathematics effectively. Approximation
operators play an important role in constructing uncertainty. Beginning at this
point, there is a connection between the approximation operators and the
topology, which is an important branch of mathematics.  In this study, the similarities of basic
topological concepts and concepts in rough set theory will be given
comparatively. The generalization of the lower and upper approximation
operators forming the dual pair in Pawlak approximation spaces and the
relations between them will be examined.

References

  • Bülbül, A. (2014) Genel Topoloji, Hacettepe Üniversitesi Yayınları, Ankara.
  • Kondo, M., Dudek, W. A. (2006). Topological structures of rough sets induced by equivalence relations. Journal of Advanced Computational Intelligence and Intelligent Informatics. 10 (5): 621- 624.
  • Kondo, M. (2006). On the structure of generalized rough sets, Information Sciences. 176: 589–600.
  • Lashin, E., Kozae, A., Khadra, A. A., Medhat, T. (2005). Rough set theory for topological spaces, International. Journal of Approximation. Reasoning. 40 (12), 35–43.
  • Li, Z., Xie, T., Li, Q. (2012). Topological structure of generalized rough sets, Comput. Math. Appl. 63,1066–1071.
  • Pawlak, Z. (1982). Rough sets, International Journal of Computer & Information Sciences 11 (5): 341–356.
  • Pawlak, Z. (1991). Rough sets: theoretical aspects of reasoning about data, Kluwer Academic Publishers, Boston.
  • Suraj, Z. (2004). An introduction to rough set theory and its applications. ICENCO 2004, December 27-30, Cairo, Egypt, 1-39.
  • Vlach, M. (2008). Algebraic and topological aspects of rough set theory. Fourth International Workshop on Computational Intelligence & Applications, IEEE SMC Hiroshima Chapter, Hiroshima University, Japan, December 10-11.
  • Yang, L., Xu, L. (2011). Topological properties of generalized approximation spaces. Information Sciences. 181: 3570-3580.
  • Yao, Y. Y. (1996). Two views of the theory of rough sets in finite universes, International Journal of Approximate Reasoning. 15 (4): 291–317.
  • Yao, Y. Y. (1998a). Constructive and algebraic methods of the theory of rough sets, Information Sciences 109: 21–47.
  • Yao , Y. Y. (1998b). Relational interpretational of neighborhood operators and rough set approximation operators, Information Sciences 111: 239–259.
  • Yao , Y. Y. (2003). On generalizing rough set theory. Proc. Int. Conf. Rough Sets Fuzzy Sets Data Min. Graul. Comput. 44-51.
  • Yu, Z. and Zhan, W. (2014). On the topological properties of generalized rough sets. Information Sciences. 263:141-152.
  • Zhu, W. (2007a). Generalized rough sets based on relations, Information Sciences. 177: 4997-5011.
  • Zhu, W. (2007b). Topological approaches to covering rough sets, Information Sciences. 177: 1499-1508.
  • Zhu, W. (2009). Relationship between generalized rough sets based on binary relation and covering, Information Sciences 179: 210–225.

Pawlak Yaklaşım Uzaylarının Topolojik Yapısı ve Genelleştirilmiş Kaba Kümeler

Year 2018, Volume: 9 Issue: Ek (Suppl.) 1, 305 - 315, 14.12.2018
https://doi.org/10.29048/makufebed.444556

Abstract

Kaba küme teorisinin temeli bilgi sistemlerine
dayanır. Bilgi sistemlerinin yapısı matematiksel anlamda özel bir bağıntı türü
olan denklik bağıntısı ile yakından ilişkilidir. Kaba küme yaklaşımı eksik ya
da belirsiz bilgiyle ilgilenir ve temel bir bilim dalı olan matematiği
merkezine alarak etkin bir şekilde kullanır. Belirsizliğin yapılandırılmasında
yaklaşım operatörleri önemli rol üstlenirler. Tam bu noktadan başlayarak,
yaklaşım operatörleri ve matematiğin önemli bir dalı olan topoloji arasında
bağlantı kurulmaktadır. Bu çalışmada temel topolojik kavramlar ile kaba küme
teorisinde yer alan kavramların benzerlikleri karşılaştırmalı olarak
verilecektir. Pawlak yaklaşım uzaylarında dual çift oluşturan alt ve üst
yaklaşım operatörlerinin genelleştirilmesi ve aralarındaki ilişkiler
incelenecektir.

References

  • Bülbül, A. (2014) Genel Topoloji, Hacettepe Üniversitesi Yayınları, Ankara.
  • Kondo, M., Dudek, W. A. (2006). Topological structures of rough sets induced by equivalence relations. Journal of Advanced Computational Intelligence and Intelligent Informatics. 10 (5): 621- 624.
  • Kondo, M. (2006). On the structure of generalized rough sets, Information Sciences. 176: 589–600.
  • Lashin, E., Kozae, A., Khadra, A. A., Medhat, T. (2005). Rough set theory for topological spaces, International. Journal of Approximation. Reasoning. 40 (12), 35–43.
  • Li, Z., Xie, T., Li, Q. (2012). Topological structure of generalized rough sets, Comput. Math. Appl. 63,1066–1071.
  • Pawlak, Z. (1982). Rough sets, International Journal of Computer & Information Sciences 11 (5): 341–356.
  • Pawlak, Z. (1991). Rough sets: theoretical aspects of reasoning about data, Kluwer Academic Publishers, Boston.
  • Suraj, Z. (2004). An introduction to rough set theory and its applications. ICENCO 2004, December 27-30, Cairo, Egypt, 1-39.
  • Vlach, M. (2008). Algebraic and topological aspects of rough set theory. Fourth International Workshop on Computational Intelligence & Applications, IEEE SMC Hiroshima Chapter, Hiroshima University, Japan, December 10-11.
  • Yang, L., Xu, L. (2011). Topological properties of generalized approximation spaces. Information Sciences. 181: 3570-3580.
  • Yao, Y. Y. (1996). Two views of the theory of rough sets in finite universes, International Journal of Approximate Reasoning. 15 (4): 291–317.
  • Yao, Y. Y. (1998a). Constructive and algebraic methods of the theory of rough sets, Information Sciences 109: 21–47.
  • Yao , Y. Y. (1998b). Relational interpretational of neighborhood operators and rough set approximation operators, Information Sciences 111: 239–259.
  • Yao , Y. Y. (2003). On generalizing rough set theory. Proc. Int. Conf. Rough Sets Fuzzy Sets Data Min. Graul. Comput. 44-51.
  • Yu, Z. and Zhan, W. (2014). On the topological properties of generalized rough sets. Information Sciences. 263:141-152.
  • Zhu, W. (2007a). Generalized rough sets based on relations, Information Sciences. 177: 4997-5011.
  • Zhu, W. (2007b). Topological approaches to covering rough sets, Information Sciences. 177: 1499-1508.
  • Zhu, W. (2009). Relationship between generalized rough sets based on binary relation and covering, Information Sciences 179: 210–225.
There are 18 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Review Paper
Authors

Sadık Bayhan 0000-0001-6100-3086

Mehmet Şen This is me 0000-0001-6100-3086

Publication Date December 14, 2018
Acceptance Date November 28, 2018
Published in Issue Year 2018 Volume: 9 Issue: Ek (Suppl.) 1

Cite

APA Bayhan, S., & Şen, M. (2018). Pawlak Yaklaşım Uzaylarının Topolojik Yapısı ve Genelleştirilmiş Kaba Kümeler. Mehmet Akif Ersoy Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 9(Ek (Suppl.) 1), 305-315. https://doi.org/10.29048/makufebed.444556