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In this paper we studied the lower and upper approximations of a rough set in a quotient group. It can be proved that under certain assumptions the lower approximation is a normal subgroup of the quotient group; however this result is not valid for the upper approximation. We developed several homomorphisms between two lower approximations of the quotient groups.<\/jats:p>","DOI":"10.3233\/jifs-162177","type":"journal-article","created":{"date-parts":[[2017,7,7]],"date-time":"2017-07-07T11:47:50Z","timestamp":1499428070000},"page":"2585-2594","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":8,"title":["The lower and upper approximations and homomorphisms between lower approximations in quotient groups"],"prefix":"10.1177","volume":"33","author":[{"given":"Waqas","family":"Mahmood","sequence":"first","affiliation":[{"name":"Department of Mathematics, Quaid-I-Azam University Islamabad, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Waqas","family":"Nazeer","sequence":"additional","affiliation":[{"name":"Division of Science and Technology, University of Education, Lahore, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shin Min","family":"Kang","sequence":"additional","affiliation":[{"name":"Department of Mathematics and RINS, Gyeongsang National University, Jinju, Korea"},{"name":"Center for General Education, China Medical University, Taichung, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2017,7,7]]},"reference":[{"key":"e_1_3_2_2_2","volume-title":"Third International Conference on Advanced Computer Theory and Engineering","author":"Bi-Cai X.","year":"2010","unstructured":"Bi-CaiX., Anti-homorphism on a group and its applications, Third International Conference on Advanced Computer Theory and Engineering, 2010."},{"key":"e_1_3_2_3_2","first-page":"251","article-title":"Rough groups and rough subgroups","volume":"42","author":"Biswas R.","year":"1994","unstructured":"BiswasR. and NandaS., Rough groups and rough subgroups, Bull Polish Acad Sci Math42 (1994), 251\u2013254.","journal-title":"Bull Polish Acad Sci Math"},{"key":"e_1_3_2_4_2","first-page":"242","volume-title":"Rough sets, fuzzy sets and knowledge discovery","author":"Bonikowaski Z.","year":"1995","unstructured":"BonikowaskiZ., Algebraic structures of rough sets, In ZiarkoW.P. 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