The Upper and Lower Approximations in Rough Subgroupoid of a Groupoid

[1] X. Liang, D. Li, On Rough Subgroup of a Group, Formalized Mathematics, 17 (2009) 213-217.10.2478/v10037-009-0026-6Search in Google Scholar

[2] Z. Pawlak, Rough sets, Int. J. Comput. Inform. Sci., 11 (1982) 341-356.10.1007/BF01001956Search in Google Scholar

[3] N. Kuroki, P.P. Wang, The lower and upper approximations in a fuzzy group, Inform. Sci., 90 (1996) 203-220.10.1016/0020-0255(95)00282-0Search in Google Scholar

[4] C.Z. Wang, D.G. Chen, A short note on some properties of rough groups, Comput. and Math. with Appl., 59 (2010) 431-436.10.1016/j.camwa.2009.06.024Search in Google Scholar

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

[6] Z. Wang, L. Shu, The lower and upper approximations in a group, Engineering and Technology, 68 (2012) 8-28.Search in Google Scholar

[7] 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

[8] D. Miao, S. Han, D. Li, L. Sun, Rough Group, Rough Subgroup and Their Properties, (2005) 104-113.10.1007/11548669_11Search in Google Scholar

[9] G. Oguz, I. Icen, M.H. Gursoy, Lie rough groups, Filomat, 32 (2018) 5735-5741.10.2298/FIL1816735OSearch in Google Scholar

[10] N. Bagirmaz, A.F. Ozcan, I. Icen, Topological Rough Groups, Topological Algebra and its Applications, 4 (2016) 31-38.10.1515/taa-2016-0004Search in Google Scholar

[11] H. Brandt, ber eine Verallgemeinerung des Gruppenbegriffes, Mathematische Annalen, 96 (1926) 360-366.10.1007/BF01209171Search in Google Scholar

[12] A. Grothendieck, T.L. Verdier, Theorie des topos, Lectures Notes Maths, Springer, 1972.10.1007/BFb0081555Search in Google Scholar

[13] R. Brown, Topology: A geometric account of general topology, homotopy types and the fundamental groupoid, Ellis, Horwood Chichester, 1988.Search in Google Scholar

[14] I.Icen, Sheaves and Local Subgroupoids, arXiv:math/0009086v2.Search in Google Scholar

[15] R. Brown, I. Icen, O. Lie local subgroupoids and their holonomy and monodromy lie groupoids, Topology Appl., 115 (2001) 125-138.10.1016/S0166-8641(00)00062-6Search in Google Scholar

[16] R. Brown, I. Icen, O. Mucuk, Local subgroupoids II:Examples and properties, Topology Apply., 127 (2003) 393-408.10.1016/S0166-8641(02)00101-3Search in Google Scholar

[17] M.R. Buneci, Approximations for uniformly continous functions on groupoids, Surv. Math. Appl., 12 (2017) 219-227.Search in Google Scholar

[18] M.H. Grsoy, H. Aslan, I. Icen, Generalized crossed modules and group-groupoids, Turkish Journal of Mathematics, 41 (2017).10.3906/mat-1602-63Search in Google Scholar

[19] Y.H. Kim, H.S. Kim, J. Neggers, Selective groupoids and frameworks induced by fuzzy subsets, Iran Journal Fuzzy System, 14 (2017) 151-160.Search in Google Scholar

[20] M.R. Buneci, A Urysohn type lemma for groupoids, Theory Appl. Categ., 32 (2017) 970-994.Search in Google Scholar

[21] M.H. Grsoy, I. Icen, Coverings of Structured Lie Groupoids, Hacettepe Journal of Mathematics ans Statistic, 47 (2018) 845-854.Search in Google Scholar

[22] I. Chadja, H. Lnger, Groupoids corresponding to relational systems, Miskolc Math. Notes, 17 (2016) 111-118.10.18514/MMN.2016.818Search in Google Scholar

[23] M.H. Grsoy, I. Icen, The homomorphisms of topological groupoids, Novi Sad J Math., 44 (2014) 129-141.Search in Google Scholar

[24] M.R. Buneci, Morphisms which are continuous on a neighborhood of the base of a groupoid, Studia Sci. Math. Hungar., 42 (2005) 265-276.10.1556/sscmath.42.2005.3.2Search in Google Scholar

[25] P.J. Higgins, Categories and Groupoids, Reprints in Theory and Applications of Categories, 7 (1971) 1-195.Search in Google Scholar