Araştırma Makalesi
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Rough Approximation Operators in a Topological Ring

Yıl 2020, , 144 - 151, 20.03.2020
https://doi.org/10.18185/erzifbed.644343

Öz

The goal of this article is to examine
the concept of topological ring from the perspective of the rough set theory
and to introduce the  approximation
operators in a topological ring with respect to its ideal. Moreover, the
definitions of lower topological rough subring and upper topological rough
subring are presented. After that, the notion of topological rough ring is
described and some related properties are studied.

Kaynakça

  • Pawlak, Z. 1982. Rough sets. Int. J. Comput. Inform. Sci., 11: 341-356.
  • Zadeh, L. A. 1965. Fuzzy sets. Inform. Control. 8: 338-353.
  • Molodtsov, D. A.1999. Soft set theory-First results. Comput. Math. Appl. 37:19-31.
  • Wiweger, R. 1989. On Topological Rough Sets. Bull. Pol. Ac. Math.37: 89-93.
  • Biswas, R, Nanda S.1994. Rough groups and rough subgroups. Bull. Pol. Acad. Sci. Math. 42: 251-254.
  • Bagirmaz, N, Icen, I, Ozcan, A.F. 2016.Topological Rough Groups. Topol. Algebra Appl. .4: 31-38.
  • Kuroki, N, Mordeson, J.N.1997. Structure of rough sets and rough groups. J. Fuzzy Math. 5:183-191.
  • Davvaz, B. 2004. Roughness in rings. Inform. Sci; 164: 147-163.
  • Kuroki, N.1997. Rough ideals in semigroups. Inform. Sci; 100:139-163.
  • Davvaz, B, Mahdavipour, M. 2006. Roughness in modules. Inform. Sci; 176: 3658-3674.
  • Wiweger, A. 1998. On topological rough sets. Bull. Polish Acad. Sci. Math; 37: 51-62.
  • Lashin, E.F, Kozae, A. M, Abo Khadra, A.A, Medhat, T. 2005. Rough set theory for topological spaces. Int. J. Aprrox. Reason; 40: 35-43.
  • Li, Z, Xie, T, Li, Q. 2012. Topological structure of generalized rough sets. Comput. Math. with Appl; 63: 1066-1071.
  • Oguz, G, Icen I, Gursoy, M.H. 2018. Lie Rough Groups. Filomat; 32: 5735-5741.
  • Miao, D, Han, S, Li, D, Sun, L. 2005. Rough Group, Rough Subgroup and Their Properties. LNCS; 3641: 104-113.
  • Iwinski J.1987. Algebraic approach to rough sets. Bull Polish Acad Sci Math; 35 : 673-683.
  • Wu, Q, Wang, T, Huang , Y, Li, J. 2008. Topology Theory on Rough Sets. IEEE Transactions on Systems, Man and Cybernetics;38: 68-77.

Bir Topolojik Halkada Kaba Yaklaşım Operatörleri

Yıl 2020, , 144 - 151, 20.03.2020
https://doi.org/10.18185/erzifbed.644343

Öz

Bu çalışmanın amacı, topolojik halka kavramını kaba küme teorisindeki bakış
açısıyla inceleyerek  bir topolojik
halkada idealine göre alt ve üst yaklaşımları tanıtmaktır. Ayrıca, alt
topolojik kaba alt halka ve üst topolojik kaba alt halka tanımları sunulmuştur.
Sonrasında, topolojik kaba halka kavramı tanımlanarak ilgili bazı özellikler
incelenmiştir.

Kaynakça

  • Pawlak, Z. 1982. Rough sets. Int. J. Comput. Inform. Sci., 11: 341-356.
  • Zadeh, L. A. 1965. Fuzzy sets. Inform. Control. 8: 338-353.
  • Molodtsov, D. A.1999. Soft set theory-First results. Comput. Math. Appl. 37:19-31.
  • Wiweger, R. 1989. On Topological Rough Sets. Bull. Pol. Ac. Math.37: 89-93.
  • Biswas, R, Nanda S.1994. Rough groups and rough subgroups. Bull. Pol. Acad. Sci. Math. 42: 251-254.
  • Bagirmaz, N, Icen, I, Ozcan, A.F. 2016.Topological Rough Groups. Topol. Algebra Appl. .4: 31-38.
  • Kuroki, N, Mordeson, J.N.1997. Structure of rough sets and rough groups. J. Fuzzy Math. 5:183-191.
  • Davvaz, B. 2004. Roughness in rings. Inform. Sci; 164: 147-163.
  • Kuroki, N.1997. Rough ideals in semigroups. Inform. Sci; 100:139-163.
  • Davvaz, B, Mahdavipour, M. 2006. Roughness in modules. Inform. Sci; 176: 3658-3674.
  • Wiweger, A. 1998. On topological rough sets. Bull. Polish Acad. Sci. Math; 37: 51-62.
  • Lashin, E.F, Kozae, A. M, Abo Khadra, A.A, Medhat, T. 2005. Rough set theory for topological spaces. Int. J. Aprrox. Reason; 40: 35-43.
  • Li, Z, Xie, T, Li, Q. 2012. Topological structure of generalized rough sets. Comput. Math. with Appl; 63: 1066-1071.
  • Oguz, G, Icen I, Gursoy, M.H. 2018. Lie Rough Groups. Filomat; 32: 5735-5741.
  • Miao, D, Han, S, Li, D, Sun, L. 2005. Rough Group, Rough Subgroup and Their Properties. LNCS; 3641: 104-113.
  • Iwinski J.1987. Algebraic approach to rough sets. Bull Polish Acad Sci Math; 35 : 673-683.
  • Wu, Q, Wang, T, Huang , Y, Li, J. 2008. Topology Theory on Rough Sets. IEEE Transactions on Systems, Man and Cybernetics;38: 68-77.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Gülay Oğuz 0000-0003-4302-8401

Yayımlanma Tarihi 20 Mart 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA Oğuz, G. (2020). Rough Approximation Operators in a Topological Ring. Erzincan University Journal of Science and Technology, 13(1), 144-151. https://doi.org/10.18185/erzifbed.644343