Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 30, 2016

Topological Rough Groups

  • Nurettin Bağırmaz , İlhan İçen and Abdullah F. Özcan

Abstract

The concept of topological group is a simple combination of the concepts of abstract group and topological space. The purpose of this paper is to combine the concepts of topological space and rough groups; called topological rough groups on an approximation space.

References

[1] A. A. Allam, M. Y. Bakeir, E. A. Abo-Tabl, Some Methods for Generating Topologies by Relations, Bull.Malays.Math. Sci. Soc. (2) 31(1) (2008), 35–45. Search in Google Scholar

[2] N. Bağırmaz, A. F. Özcan, Rough semigroups on approximation spaces, International Journal of Algebra, Vol. 9, 2015, no. 7, 339-350. 10.12988/ija.2015.5742Search in Google Scholar

[3] R. Biswas, S. Nanda, Rough groups and rough subgroups, Bull. Polish Acad. Sci. Math 42 (1994) 251–254. Search in Google Scholar

[4] Z. Bonikowaski, Algebraic structures of rough sets, in: W.P. Ziarko (Ed.), Rough Sets, Fuzzy Sets and Knowledge Discovery, Springer-Verlag, Berlin, 1995, pp. 242–247. 10.1007/978-1-4471-3238-7_29Search in Google Scholar

[5] W. Cheng, Z.Mo, J.Wang, Notes on “the lower and upper approximations in a fuzzy group” and “rough ideals in semigroups”, Inform. Sci. 177(2007)5134-5140. Search in Google Scholar

[6] B. Davvaz, Roughness in rings, Inform. Sci. 164 (2004) 147–163. 10.1016/j.ins.2003.10.001Search in Google Scholar

[7] T. Iwinski, Algebraic approach to rough sets, Bull. Polish Acad. Sci. Math. 35 (1987) 673–683. Search in Google Scholar

[8] J. Jarvinen, Properties of Rough Approximations, J. Adv. Comput. Intel. and Intelligent Inform. Vol.9 No.5 (2005) 502-505. 10.20965/jaciii.2005.p0502Search in Google Scholar

[9] J. Jarvinen, On the Structure of Rough Approximations, Fund. Inform.53 (2002) 135-153. Search in Google Scholar

[10] M. Kondo, On the structure of generalized rough sets, Inform. Sci. 176 (2006) 589–600. 10.1016/j.ins.2005.01.001Search in Google Scholar

[11] N. Kuroki, P.P. Wang, The lower and upper approximations in a fuzzy group, Information Sciences 90 (1996) 203–220. 10.1016/0020-0255(95)00282-0Search in Google Scholar

[12] N. Kuroki, Rough ideals in semigroups, Inform. Sci. 100 (1997) 139–163. 10.1016/S0020-0255(96)00274-5Search in Google Scholar

[13] E.F. Lashin et al, Rough set theory for topological spaces, Int. J. Aprrox. Reason. 40 (2005) 35–43. 10.1016/j.ijar.2004.11.007Search in Google Scholar

[14] F. Li, Z. Zhang, The Homomorphisms and Operations of Rough Groups, The Scientific World Journal, Volume 2014, Article ID 507972, 6 pages. 10.1155/2014/507972Search in Google Scholar PubMed PubMed Central

[15] Z. Li, T. Xie, Q. Li, Topological structure of generalized rough sets, Comput. Math. with Appl. 63 (2012) 1066–1071. 10.1016/j.camwa.2011.12.011Search in Google Scholar

[16] D. Miao, S. Han, D. Li, and L. Sun, Rough Group, Rough Subgroup and Their Properties, D. Ślkezak et al. (Eds.): RSFDGrC 2005, LNAI 3641, pp. 104–113, 2005.© Springer-Verlag Berlin Heidelberg 2005. 10.1007/11548669_11Search in Google Scholar

[17] A. F. Özcan, N. Bağırmaz, H. Taşbozan, İ. İçen, Topologies and Approximation Operators Induced by Binary Relations, IECMSA-2013, Sarajevo, Bosnıa and Herzegovina, August 2013. Search in Google Scholar

[18] Z. Pawlak, Rough sets, Int. J. Comput. Inform. Sci. 11 (1982) 341–356. 10.1007/BF01001956Search in Google Scholar

[19] Z. Pawlak, Rough sets and intelligent data analysis, Inform. Sci. 147 (2002) 1-12. 10.1016/S0020-0255(02)00197-4Search in Google Scholar

[20] Z. Pei, D. Pei , L. Zheng, Topology vs generalized rough sets, Int. J. Aprrox. Reason. 52 (2011) 231–239. 10.1016/j.ijar.2010.07.010Search in Google Scholar

[21] L. Polkowski and A. Skowron, Eds., Rough Sets and Current Trends in Computing, vol. 1424, Springer,Berlin, Germany, 1998. Search in Google Scholar

[22] J. Pomykala, J.A. Pomykala, The stone algebra of rough sets, Bull. Polish Acad. Sci. Math. 36 (1998) 495–508. Search in Google Scholar

[23] Pontryagin, Lev S., Topological groups , Princeton Univ. Press (1958) (Translated from Russian). Search in Google Scholar

[24] A.S. Salama, M.M.E. Abd El-Monsef, New topological approach of rough set generalizations, Internat. J. Computer Math. Vol. 8, No.7, (2011) 1347-1357. Search in Google Scholar

[25] A. Skowron, On the topology in information systems, Bull. Polish Acad. Sci. Math. 36 (1988) 477–480. Search in Google Scholar

[26] M. L. Thivagar, C. Richard, N. R. Paul,Mathematical Innovations of a Modern Topology in Medical Events, Internat. J. Inform. Sci. 2(4) (2012) 33-36. 10.5923/j.ijis.20120204.01Search in Google Scholar

[27] C.Z. Wang, D.G. Chen, A short note on some properties of rough groups, Comput. Math. Appl. 59(2010)431-436. Search in Google Scholar

[28] Z. Wang, L. Shu, The lower and upper approximations in a group, International Journal of Mathematical and Computational Sciences, 6 (2012),158-162. Search in Google Scholar

[29] C.Wang, D. Chen, Q. Hu, On rough approximations of groups, Int. J.Mach. Learn. & Cyber. DOI 10.1007/s13042-012-0108-6, Springer-Verlag 2012. Search in Google Scholar

[30] M. Vlach, Algebraic and Topological Aspects of Rough Set Theory, Fourth International Workshop on Computational Intelligence Applications, IEEE SCM Hiroshima Chapter, Hiroshima University, Japan, December, 2008. Search in Google Scholar

[31] A. Wiweger, On topological rough sets, Bull. Polish Acad. Sci. Math. 37 (1988) 51–62. Search in Google Scholar

Received: 2016-2-5
Accepted: 2016-12-13
Published Online: 2016-12-30

© 2016 Nurettin Bağırmaz et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 22.5.2024 from https://www.degruyter.com/document/doi/10.1515/taa-2016-0004/html
Scroll to top button