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First, two pairs of SSs are established by adopting an SBR to approximate a soft subset, and their unique axiomatic systems are analyzed. Two varieties of soft topologies derived from soft reflexive relations (SRRs) are also inspected. Besides, several similarity relations associated with SBRS are also explored. We next devise a decision-making methodology within the environment of the endorsed approach. In addition, we\u00a0provide\u00a0the two decision-making algorithms. Eventually, an applied example is implemented to evaluate the reliability and practicality of the decision processes. An extensive comparison study confirms the projected method\u2019s feasibility and superiority over existing approaches to decision-making.<\/jats:p>","DOI":"10.1142\/s179300572650064x","type":"journal-article","created":{"date-parts":[[2025,3,20]],"date-time":"2025-03-20T03:35:59Z","timestamp":1742441759000},"page":"1269-1301","source":"Crossref","is-referenced-by-count":4,"title":["A Novel Scheme of Roughness of Soft Sets Under Soft Binary Relations and Its Applications in Decision Analysis"],"prefix":"10.1142","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-2424-4971","authenticated-orcid":false,"given":"Rani Sumaira","family":"Kanwal","sequence":"first","affiliation":[{"name":"Department of Mathematics, Government College Women University, Faisalabad 38000, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4732-3320","authenticated-orcid":false,"given":"Saqib Mazher","family":"Qurashi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6139-1872","authenticated-orcid":false,"given":"Rizwan","family":"Gul","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad 44230, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2025,6,14]]},"reference":[{"key":"S179300572650064XBIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2011.01.003"},{"key":"S179300572650064XBIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2012.01.002"},{"key":"S179300572650064XBIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.11.009"},{"key":"S179300572650064XBIB004","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2022.3218695"},{"key":"S179300572650064XBIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2010.03.015"},{"key":"S179300572650064XBIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2010.05.004"},{"key":"S179300572650064XBIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2004.10.036"},{"key":"S179300572650064XBIB008","first-page":"589","volume":"9","author":"Maji P. 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