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Year 2019, Volume: 20 Issue: 3, 307 - 316, 26.09.2019
https://doi.org/10.18038/estubtda.508774

Abstract

References

  • [1] Pawlak Z. Rough sets, Int J Comput Inform Sci 1982; 11: 341-356.
  • [2] Pawlak Z. Rough sets and intelligent data analysis, Inform Sci 2002; 147(1-4): 1-12.
  • [3] Pawlak Z, Skowron A. Rough sets and Boolean reasoning. Inform Sci 2007; 177(1): 41-73.
  • [4] Zhan J, Liu Q, Herawan T. A novel soft rough set: Soft rough hemirings and correspondingmulticriteria group decision making, Applied Soft Computing 2017; 54: 393-402.
  • [5] Bonikowski Z. Algebraic structures of rough sets, in: W.P. Ziarko (Ed.), Rough Sets, Fuzzy Sets and Knowledge Discovery, Springer-Verlag, Berlin, 1995, pp. 242-247.
  • [6] Iwinski T. Algebraic approach to rough sets, Bull Polish Acad Sci Math 1987; 35: 673-683.
  • [7] Pomykala J, Pomykala J. A. The stone algebra of rough sets, Bull Polish Acad Sci Math 1998 ; 36: 495-508.
  • [8] Kuroki N, Wang P. P. The lower and upper approximations in a fuzzy group, Inform Sci 1996; 90: 203-220.
  • [9] Bağırmaz N, Özcan A F, İçen İ. Rough Approximations in a Topological Group, Gen Math Notes 2016; 36(2): 1-18.
  • [10] Cheng W, Mo Z, Wang J. Notes on "the lower and upper approximations in a fuzzy group" and "rough ideals in semigroups", Inform Sci 2007; 177: 5134-5140.
  • [11] Wang C, Chen D. A short note on some properties of rough groups, Comput Math Appl 2010; 59: 431-436.
  • [12] Wang C, Chen D, Hu Q. On rough approximations of groups, Int J Mach Learn & Cyber, 2013; 4(5): 445–449.
  • [13] Wang Z, Shu L. The lower and upper approximations in a grop, International Journal of Mathematical and Computational Sciences 2012; 6: 158-162.
  • [14] Li F, Zhang Z. The Homomorphisms and Operations of Rough Groups, The Scientific World Journal, Volume 2014, Article ID 507972, 6 pages.
  • [15] Biswas R, Nanda S. Rough groups and rough subgroups, Bull Polish Acad Sci Math 1994; 42: 251-254.
  • [16] Miao D, Han S, Li D, and Sun L. 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.
  • [17] Bağırmaz N, Özcan A F. Rough semigroups on approximation spaces, International Journal of Algebra 2015; 9(7): 339-350.
  • [19] Feyzioğlu A. K. A course on algebra, Boğaziçi University Publication, İstanbul, 1990.

DIRECT PRODUCTS OF ROUGH SUBGROUPS

Year 2019, Volume: 20 Issue: 3, 307 - 316, 26.09.2019
https://doi.org/10.18038/estubtda.508774

Abstract



In this study, we have defined the
concepts of direct products of the rough approximations and rough subgroups in
a group. We have given some basic features about the subject described in the
present article and we have also examined the homomorphic images of these
structures.




References

  • [1] Pawlak Z. Rough sets, Int J Comput Inform Sci 1982; 11: 341-356.
  • [2] Pawlak Z. Rough sets and intelligent data analysis, Inform Sci 2002; 147(1-4): 1-12.
  • [3] Pawlak Z, Skowron A. Rough sets and Boolean reasoning. Inform Sci 2007; 177(1): 41-73.
  • [4] Zhan J, Liu Q, Herawan T. A novel soft rough set: Soft rough hemirings and correspondingmulticriteria group decision making, Applied Soft Computing 2017; 54: 393-402.
  • [5] Bonikowski Z. Algebraic structures of rough sets, in: W.P. Ziarko (Ed.), Rough Sets, Fuzzy Sets and Knowledge Discovery, Springer-Verlag, Berlin, 1995, pp. 242-247.
  • [6] Iwinski T. Algebraic approach to rough sets, Bull Polish Acad Sci Math 1987; 35: 673-683.
  • [7] Pomykala J, Pomykala J. A. The stone algebra of rough sets, Bull Polish Acad Sci Math 1998 ; 36: 495-508.
  • [8] Kuroki N, Wang P. P. The lower and upper approximations in a fuzzy group, Inform Sci 1996; 90: 203-220.
  • [9] Bağırmaz N, Özcan A F, İçen İ. Rough Approximations in a Topological Group, Gen Math Notes 2016; 36(2): 1-18.
  • [10] Cheng W, Mo Z, Wang J. Notes on "the lower and upper approximations in a fuzzy group" and "rough ideals in semigroups", Inform Sci 2007; 177: 5134-5140.
  • [11] Wang C, Chen D. A short note on some properties of rough groups, Comput Math Appl 2010; 59: 431-436.
  • [12] Wang C, Chen D, Hu Q. On rough approximations of groups, Int J Mach Learn & Cyber, 2013; 4(5): 445–449.
  • [13] Wang Z, Shu L. The lower and upper approximations in a grop, International Journal of Mathematical and Computational Sciences 2012; 6: 158-162.
  • [14] Li F, Zhang Z. The Homomorphisms and Operations of Rough Groups, The Scientific World Journal, Volume 2014, Article ID 507972, 6 pages.
  • [15] Biswas R, Nanda S. Rough groups and rough subgroups, Bull Polish Acad Sci Math 1994; 42: 251-254.
  • [16] Miao D, Han S, Li D, and Sun L. 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.
  • [17] Bağırmaz N, Özcan A F. Rough semigroups on approximation spaces, International Journal of Algebra 2015; 9(7): 339-350.
  • [19] Feyzioğlu A. K. A course on algebra, Boğaziçi University Publication, İstanbul, 1990.
There are 18 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Nurettin Bağırmaz 0000-0002-7663-3002

Publication Date September 26, 2019
Published in Issue Year 2019 Volume: 20 Issue: 3

Cite

AMA Bağırmaz N. DIRECT PRODUCTS OF ROUGH SUBGROUPS. Estuscience - Se. September 2019;20(3):307-316. doi:10.18038/estubtda.508774