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Also, we have analyzed the roughness in the bipolar fuzzy subsemigroup (BF-SSG) by employing a congruence relation (CR) defined on the SG and investigating several related characteristics. Further, the idea is expanded to the rough fuzzy bipolar soft ideal, rough fuzzy bipolar soft interior ideal, and rough fuzzy bipolar soft bi-ideal in SGs. Moreover, it is observed that CR and complete CR (CCR) are critical in developing rough approximations of fuzzy bipolar soft ideals. Therefore, their related characteristics are studied via CRs and CCRs. <\/jats:p>","DOI":"10.1142\/s179300572550019x","type":"journal-article","created":{"date-parts":[[2024,2,3]],"date-time":"2024-02-03T06:04:40Z","timestamp":1706940280000},"page":"415-455","source":"Crossref","is-referenced-by-count":3,"title":["A Study on Rough Fuzzy Bipolar Soft Ideals in Semigroups"],"prefix":"10.1142","volume":"21","author":[{"given":"Nosheen","family":"Malik","sequence":"first","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad","family":"Shabir","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rizwan","family":"Gul","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2024,4,26]]},"reference":[{"key":"S179300572550019XBIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"S179300572550019XBIB002","doi-asserted-by":"publisher","DOI":"10.3390\/sym15020471"},{"key":"S179300572550019XBIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s40747-022-00878-4"},{"key":"S179300572550019XBIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-009-0465-6"},{"key":"S179300572550019XBIB005","doi-asserted-by":"publisher","DOI":"10.1155\/2023\/1487724"},{"key":"S179300572550019XBIB006","doi-asserted-by":"publisher","DOI":"10.1007\/BF01001956"},{"key":"S179300572550019XBIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2014.10.006"},{"key":"S179300572550019XBIB008","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(98)10006-3"},{"key":"S179300572550019XBIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2007.05.037"},{"key":"S179300572550019XBIB010","doi-asserted-by":"publisher","DOI":"10.1080\/03081079008935107"},{"key":"S179300572550019XBIB011","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(99)00056-5"},{"key":"S179300572550019XBIB012","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(03)00016-6"},{"key":"S179300572550019XBIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2010.05.004"},{"key":"S179300572550019XBIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.11.009"},{"key":"S179300572550019XBIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.03.011"},{"key":"S179300572550019XBIB016","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(71)90199-5"},{"key":"S179300572550019XBIB017","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(91)90037-U"},{"key":"S179300572550019XBIB018","first-page":"32","volume":"26","author":"Hussain A.","year":"2019","journal-title":"Journal of New Theory"},{"key":"S179300572550019XBIB019","first-page":"251","volume":"42","author":"Biswas R.","year":"1994","journal-title":"Bulletin of the Polish Academy of Sciences Mathematics"},{"key":"S179300572550019XBIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.12.008"},{"key":"S179300572550019XBIB021","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.05.050"},{"key":"S179300572550019XBIB022","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200810030"},{"key":"S179300572550019XBIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2010.03.034"},{"key":"S179300572550019XBIB024","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.07.047"},{"key":"S179300572550019XBIB025","first-page":"305","volume-title":"Proc. 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