{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T19:10:54Z","timestamp":1776280254005,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,24]],"date-time":"2023-12-24T00:00:00Z","timestamp":1703376000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The aim of this paper is to give an interesting connection between two mathematical approaches to vagueness: binary bipolar soft sets and binary bipolar soft topology. The binary bipolar soft points are defined using binary bipolar soft sets. The binary bipolar soft set will be the binary bipolar soft union of its binary bipolar soft points. Moreover, the notion of binary bipolar soft topological spaces over two universal sets and a parameter set is proposed. Some topological properties of binary bipolar soft sets, such as binary bipolar soft open, binary bipolar soft closed, binary bipolar soft closure, binary bipolar soft interior, and binary bipolar soft boundary, are introduced. Some important properties of these classes of binary bipolar soft sets are investigated. Furthermore, the symmetry relation is compared between binary bipolar soft topology and binary soft topology on a common universe set. Finally, some results and counterexamples are demonstrated to explain this work.<\/jats:p>","DOI":"10.3390\/sym16010023","type":"journal-article","created":{"date-parts":[[2023,12,24]],"date-time":"2023-12-24T20:44:15Z","timestamp":1703450655000},"page":"23","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Binary Bipolar Soft Points and Topology on Binary Bipolar Soft Sets with Their Symmetric Properties"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1055-9399","authenticated-orcid":false,"given":"Hind Y.","family":"Saleh","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Basic Education, University of Duhok, Duhok 42001, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Areen A.","family":"Salih","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul 41001, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2049-2044","authenticated-orcid":false,"given":"Baravan A.","family":"Asaad","sequence":"additional","affiliation":[{"name":"Department of Computer Science, College of Science, Cihan University-Duhok, Duhok 42001, Iraq"},{"name":"Department of Mathematics, Faculty of Science, University of Zakho, Zakho 42002, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1085-4504","authenticated-orcid":false,"given":"Ramadhan A.","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Basic Education, University of Duhok, Duhok 42001, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S0898-1221(99)00056-5","article-title":"Soft set theory-first results","volume":"37","author":"Molodtsov","year":"1999","journal-title":"Comput. 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