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Moreover, generalization of rough multiset model by defining new multiset approximation operators in more general setting via multiset ideal has been presented. The concepts of lower and upper multiset approximations via multiset ideals have been mentioned. These new definitions decrease the upper multiset approximation and increase the lower multiset approximation and hence decreasing the boundary region and increasing the accuracy measure. Properties of these multiset approximations are studied and various examples are mentioned. Also, the comparison between the rough multiset approximations defined by Girish and John [11, 12] and the current multiset approximations has been presented. It\u2019s therefore shown that the current definitions are more generally. Finally, the multiset topology induced by the present methods is finer than the multiset topology induced by the old method [11, 12].<\/jats:p>","DOI":"10.3233\/ifs-151891","type":"journal-article","created":{"date-parts":[[2016,3,1]],"date-time":"2016-03-01T10:50:08Z","timestamp":1456829408000},"page":"1791-1802","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":10,"title":["Generalized rough multiset via multiset ideals"],"prefix":"10.1177","volume":"30","author":[{"given":"Amr","family":"Zakaria","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.J.","family":"John","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Institute of Technology Calicut, Calicut, Kerala, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.A.","family":"El-Sheikh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2016,2,8]]},"reference":[{"key":"e_1_3_1_2_2","first-page":"36","article-title":"Multiset theory","volume":"30","author":"Blizard W.D.","year":"1989","unstructured":"BlizardW.D., Multiset theory, Notre Dame J Form Log 30 (1989), 36\u201365.","journal-title":"Notre Dame J Form Log"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093635499"},{"key":"e_1_3_1_4_2","first-page":"181","article-title":"The rule induction system LERS - A version for personal computers","volume":"18","author":"Chmielewski M.R.","year":"1993","unstructured":"ChmielewskiM.R., Grzymala-BusseJ.W., PetersonN.W. and ThanS., The rule induction system LERS - A version for personal computers, Found Comput Decision Sci 18 (1993), 181\u2013212.","journal-title":"Found Comput Decision Sci"},{"key":"e_1_3_1_5_2","first-page":"1","article-title":"On Yager\u2019s theory of bags and fuzzy bags","volume":"18","author":"Chakrabarty K.","year":"1999","unstructured":"ChakrabartyK., BiswasR. and NandaS., On Yager\u2019s theory of bags and fuzzy bags, Computers and Artificial Intelligence 18 (1999), 1\u201317.","journal-title":"Computers and Artificial Intelligence"},{"key":"e_1_3_1_6_2","first-page":"23","article-title":"Bags with interval counts","volume":"25","author":"Chakrabarty K.","year":"2000","unstructured":"ChakrabartyK., Bags with interval counts, Found Comput Decis Sci 25 (2000), 23\u201336.","journal-title":"Found Comput Decis Sci"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.20195"},{"key":"e_1_3_1_8_2","first-page":"235","article-title":"Note on rough multiset and its multiset topology","volume":"10","author":"El-Sheikh S.A.","year":"2015","unstructured":"El-SheikhS.A. and ZakariaA., Note on rough multiset and its multiset topology, Ann Fuzzy Math Inform 10 (2015), 235\u2013238.","journal-title":"Ann Fuzzy Math Inform"},{"key":"e_1_3_1_9_2","first-page":"193","article-title":"General relations between partially ordered multisets and their chains and antichains","volume":"14","author":"Girish K.P.","year":"2009","unstructured":"GirishK.P. and JohnS.J., General relations between partially ordered multisets and their chains and antichains, Math Commun 14 (2009), 193\u2013206.","journal-title":"Math Commun"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2008.11.002"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1155\/2011-495392"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-21563-6_4"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.11.023"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1990.11995593"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(01)00066-4"},{"key":"e_1_3_1_16_2","first-page":"525","article-title":"Generalized rough sets via ideals","volume":"5","author":"Kandil A.","year":"2013","unstructured":"KandilA., YakoutM.M. and ZakariaA., Generalized rough sets via ideals, Ann Fuzzy Math Inform 5 (2013), 525\u2013532.","journal-title":"Ann Fuzzy Math Inform"},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(98)10019-1"},{"key":"e_1_3_1_18_2","unstructured":"KuratowskiK. 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