TY - JOUR T1 - Rough Approximation Operators in a Topological Ring TT - Bir Topolojik Halkada Kaba Yaklaşım Operatörleri AU - Oğuz, Gülay PY - 2020 DA - March DO - 10.18185/erzifbed.644343 JF - Erzincan University Journal of Science and Technology PB - Erzincan Binali Yildirim University WT - DergiPark SN - 2149-4584 SP - 144 EP - 151 VL - 13 IS - 1 LA - en AB - The goal of this article is to examinethe concept of topological ring from the perspective of the rough set theoryand to introduce the approximationoperators in a topological ring with respect to its ideal. Moreover, thedefinitions of lower topological rough subring and upper topological roughsubring are presented. After that, the notion of topological rough ring isdescribed and some related properties are studied. KW - Rough set KW - rough approximations KW - rough ring KW - topological rough ring N2 - Bu çalışmanın amacı, topolojik halka kavramını kaba küme teorisindeki bakışaçısıyla inceleyerek bir topolojikhalkada idealine göre alt ve üst yaklaşımları tanıtmaktır. Ayrıca, alttopolojik kaba alt halka ve üst topolojik kaba alt halka tanımları sunulmuştur.Sonrasında, topolojik kaba halka kavramı tanımlanarak ilgili bazı özelliklerincelenmiştir. CR - Pawlak, Z. 1982. Rough sets. Int. J. Comput. Inform. Sci., 11: 341-356. CR - Zadeh, L. A. 1965. Fuzzy sets. Inform. Control. 8: 338-353. CR - Molodtsov, D. A.1999. Soft set theory-First results. Comput. Math. Appl. 37:19-31. CR - Wiweger, R. 1989. On Topological Rough Sets. Bull. Pol. Ac. Math.37: 89-93. CR - Biswas, R, Nanda S.1994. Rough groups and rough subgroups. Bull. Pol. Acad. Sci. Math. 42: 251-254. CR - Bagirmaz, N, Icen, I, Ozcan, A.F. 2016.Topological Rough Groups. Topol. Algebra Appl. .4: 31-38. CR - Kuroki, N, Mordeson, J.N.1997. Structure of rough sets and rough groups. J. Fuzzy Math. 5:183-191. CR - Davvaz, B. 2004. Roughness in rings. Inform. Sci; 164: 147-163. CR - Kuroki, N.1997. Rough ideals in semigroups. Inform. Sci; 100:139-163. CR - Davvaz, B, Mahdavipour, M. 2006. Roughness in modules. Inform. Sci; 176: 3658-3674. CR - Wiweger, A. 1998. On topological rough sets. Bull. Polish Acad. Sci. Math; 37: 51-62. CR - 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. CR - Li, Z, Xie, T, Li, Q. 2012. Topological structure of generalized rough sets. Comput. Math. with Appl; 63: 1066-1071. CR - Oguz, G, Icen I, Gursoy, M.H. 2018. Lie Rough Groups. Filomat; 32: 5735-5741. CR - Miao, D, Han, S, Li, D, Sun, L. 2005. Rough Group, Rough Subgroup and Their Properties. LNCS; 3641: 104-113. CR - Iwinski J.1987. Algebraic approach to rough sets. Bull Polish Acad Sci Math; 35 : 673-683. CR - Wu, Q, Wang, T, Huang , Y, Li, J. 2008. Topology Theory on Rough Sets. IEEE Transactions on Systems, Man and Cybernetics;38: 68-77. UR - https://doi.org/10.18185/erzifbed.644343 L1 - https://dergipark.org.tr/en/download/article-file/1015427 ER -