{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T05:26:13Z","timestamp":1784784373390,"version":"3.55.0"},"reference-count":51,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,10]],"date-time":"2023-03-10T00:00:00Z","timestamp":1678406400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Faisal University","award":["3014"],"award-info":[{"award-number":["3014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Symmetry-related problems can be addressed by means of group theory, and ring theory can be seen as an extension of additive group theory. Ring theory, a significant topic in abstract algebra, is currently active in a diverse range of study domains across the disciplines of mathematics, theoretical physics and coding theory. The study of ideals is vital to the theory of rings in a wide range of ways. The uncertainties present in the information are addressed well by the q-rung orthopair fuzzy set (q-ROFS). Considering the significance of ring theory and the q-ROFS, this article defines q-rung orthopair fuzzy ideals (q-ROFIs) in conventional rings and investigates its various algebraic features. We introduce the notion of q-rung orthopair fuzzy cosets (q-ROFCs) of a q-ROFI and demonstrate that, under certain binary operations, the collection of all q-ROFCs of a q-ROFI forms a ring. In addition, we provide a q-rung orthopair analog of the fundamental theorem of ring homomorphism. Furthermore, we present the notion of q-rung orthopair fuzzy semi-prime ideals (q-ROFSPIs) and provide a comprehensive explanation of their many algebraic properties. Finally, regular rings were characterized using q-ROFIs.<\/jats:p>","DOI":"10.3390\/sym15030697","type":"journal-article","created":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T06:09:56Z","timestamp":1678687796000},"page":"697","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Detailed Study of Mathematical Rings in q-Rung Orthopair Fuzzy Framework"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7579-8972","authenticated-orcid":false,"given":"Asima","family":"Razzaque","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Al Ahsa Hofuf 31982, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1898-4082","authenticated-orcid":false,"given":"Abdul","family":"Razaq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ghaliah","family":"Alhamzi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9099-8422","authenticated-orcid":false,"given":"Harish","family":"Garg","sequence":"additional","affiliation":[{"name":"School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala 147004, Punjab, India"},{"name":"Applied Science Research Center, Applied Science Private University, Amman 11931, Jordan"},{"name":"Department of Mathematics, Graphic Era Deemed to Be University, Dehradun 248002, Uttarakhand, India"},{"name":"College of Technical Engineering, The Islamic University, Najaf 54001, Iraq"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad Iftikhar","family":"Faraz","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, King Faisal University, Al-Ahsa Hofuf 31982, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zadeh, L.A. 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